{"id":15465,"date":"2024-02-29T05:27:45","date_gmt":"2024-02-28T23:57:45","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=15465"},"modified":"2024-02-29T14:57:10","modified_gmt":"2024-02-29T09:27:10","slug":"selina-icse-solutions-class-10-maths-linear-inequations-one-variable","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/selina-icse-solutions-class-10-maths-linear-inequations-one-variable\/","title":{"rendered":"Selina Concise Mathematics Class 10 ICSE Solutions Linear Inequations (in one variable)"},"content":{"rendered":"

Selina Concise Mathematics Class 10 ICSE Solutions Linear Inequations (in one variable)<\/h2>\n

Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 4\u00a0Linear Inequations (in one variable)<\/strong><\/p>\n

Linear Inequations in One Variable Exercise 4A – Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n

Question 1.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/h3>\n

Question 2.<\/strong><\/span>
\nState, whether the following statements are true or false:
\n(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c
\n(iii) If a < b, then ac > bc
\n(iv) If a > b, then\u00a0\\(\\frac { a }{ c } <\\frac { b }{ c }\\)
\n(v) If a – c > b – d, then a + d > b + c
\n(vi) If a < b, and c > 0, then a – c > b – c
\nWhere a, b, c and d are real numbers and c \u2260 0.
\nSolution:<\/strong><\/span>
\n(i) a < b \u21d2 a – c < b – c The given statement is true.
\n(ii) If a > b \u21d2\u00a0a + c > b + c
\nThe given statement is true.
\n(iii) If a < b \u21d2\u00a0ac < bc The given statement is false.
\n(iv) If a > b\u00a0\u21d2\u00a0\\(\\frac { a }{ c } >\\frac { b }{ c }\\)
\nThe given statement is false.
\n(v) If a – c > b – d \u21d2 a + d > b + c
\nThe given statement is true.
\n(vi) If a < b \u21d2 a – c < b – c (Since, c > 0)
\nThe given statement is false.<\/p>\n

Question 3.<\/strong><\/span>
\nIf x \u2208 N, find the solution set of inequations.
\n(i) 5x + 3 \u2264 2x + 18
\n(ii) 3x – 2 < 19 – 4x
\nSolution:<\/strong><\/span>
\n(i) 5x + 3 \u2264\u00a02x + 18
\n5x – 2x \u2264\u00a018 – 3
\n3x \u2264\u00a015
\nx \u2264 5
\nSince, x \u2208 N, therefore solution set is {1, 2, 3, 4, 5}.
\n(ii) 3x – 2 < 19 – 4x
\n3x + 4x < 19 + 2
\n7x < 21
\nx < 3
\nSince, x \u2208 N, therefore solution set is {1, 2}.<\/p>\n

Question 4.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n(i) x + 7 \u2264\u00a011
\nx \u2264\u00a011 – 7
\nx \u2264\u00a04
\nSince, the replacement set = W (set of whole numbers)
\n\u21d2 Solution set = {0, 1, 2, 3, 4}
\n(ii) 3x – 1 > 8
\n3x > 8 + 1
\nx > 3
\nSince, the replacement set = W (set of whole numbers)
\n\u21d2 Solution set = {4, 5, 6, \u2026}
\n(iii) 8 – x > 5
\n– x > 5 – 8
\n– x > -3
\nx < 3
\nSince, the replacement set = W (set of whole numbers)
\n\u21d2 Solution set = {0, 1, 2}
\n\"Selina
\nSince, the replacement set = W (set of whole numbers)
\n\u2234 Solution set = {0, 1, 2}
\n\"Selina
\nSince, the replacement set = W (set of whole numbers)
\n\u2234 Solution set = {0, 1}
\n(vi) 18 \u2264 3x – 2
\n18 + 2 \u2264 3x
\n20 \u2264 3x
\nx \u2265 \\(\\frac { 20 }{ 3 }\\)
\nSince, the replacement set = W (set of whole numbers)
\n\u2234 Solution set = {7, 8, 9, \u2026}<\/p>\n

Question 5.<\/strong><\/span>
\nSolve the inequation:
\n3 – 2x \u2265 x – 12 given that x \u2208 N.
\nSolution:<\/strong><\/span>
\n3 – 2x \u2265\u00a0x – 12
\n-2x – x \u2265 -12 – 3
\n-3x \u2265\u00a0-15
\nx \u2264\u00a05
\nSince, x \u2208 N, therefore,
\nSolution set = {1, 2, 3, 4, 5}<\/p>\n

Question 6.<\/strong><\/span>
\nIf 25 – 4x \u2264 16, find:
\n(i) the smallest value of x, when x is a real number,
\n(ii) the smallest value of x, when x is an integer.
\nSolution:<\/strong><\/span>
\n25 – 4x \u2264\u00a016
\n-4x \u2264\u00a016 – 25
\n-4x \u2264\u00a0-9
\nx\u00a0\u2265\u00a0\\(\\frac { 9 }{ 4 }\\)
\nx\u00a0\u2265 2.25
\n(i) The smallest value of x, when x is a real number, is 2.25.
\n(ii) The smallest value of x, when x is an integer, is 3.<\/p>\n

Question 7.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 8.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\nThus, the required smallest value of x is -1.<\/p>\n

Question 9.<\/strong><\/span>
\nFind the largest value of x for which
\n2(x – 1) \u2264 9 – x and x \u2208 W.
\nSolution:<\/strong><\/span>
\n2(x – 1) \u2264 9 – x
\n2x – 2 \u2264 9 – x
\n2x + x \u2264 9 + 2
\n3x \u2264 11
\nx \u2264 \\(\\frac { 11 }{ 3 }\\)
\nx \u2264 3.67
\nSince, x \u2208 W, thus the required largest value of x is 3.<\/p>\n

Question 10.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 11.<\/strong><\/span>
\nGiven x \u2208 {integers}, find the solution set of:
\n-5 \u2264 2x – 3 < x + 2
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 12.<\/strong><\/span>
\nGiven x \u2208 {whole numbers}, find the solution set of:
\n-1 \u2264 3 + 4x < 23
\n
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Linear Inequations in One Variable Exercise 4B – Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n

Question 1.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 2.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 3.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 4.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 5.<\/strong><\/span>
\nx \u2208 {real numbers} and -1 < 3 – 2x \u2264 7, evaluate x and represent it on a number line.
\nSolution:<\/strong><\/span>
\n-1 < 3 – 2x \u2264\u00a07
\n-1 < 3 – 2x and 3 – 2x \u2264\u00a07
\n2x < 4 and -2x \u2264\u00a04
\nx < 2 and x \u2265\u00a0-2
\nSolution set = {-2 \u2264 x < 2, x \u2208 R}
\nThus, the solution can be represented on a number line as:
\n\"Selina<\/p>\n

Question 6.<\/strong><\/span>
\nList the elements of the solution set of the inequation
\n-3 < x – 2 \u2264 9 – 2x; x \u2208 N.
\nSolution:<\/strong><\/span>
\n-3 < x – 2 \u2264\u00a09 – 2x
\n-3 < x – 2 and x – 2 \u2264\u00a09 – 2x
\n-1 < x and 3x \u2264\u00a011
\n-1 < x\u00a0\u2264\u00a0\\(\\frac { 11 }{ 3 }\\)
\nSince, x \u2208\u00a0N
\n\u2234 Solution set = {1, 2, 3}<\/p>\n

Question 7.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 8.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\nQuestion 9.<\/strong><\/span>
\nGiven x \u2208 {real numbers}, find the range of values of x for which -5 \u2264 2x – 3 < x + 2 and represent it on a number line.
\nSolution:<\/strong><\/span>
\n-5 \u2264\u00a02x – 3 < x + 2
\n-5 \u2264\u00a02x – 3 and 2x – 3 < x + 2
\n-2 \u2264\u00a02x and x < 5
\n-1 \u2264\u00a0x and x < 5
\nRequired range is -1 \u2264\u00a0x < 5.
\nThe required graph is:
\n\"Selina<\/p>\n

Question 10.<\/strong><\/span>
\nIf 5x – 3 \u2264 5 + 3x \u2264 4x + 2, express it as a \u2264 x \u2264 b and then state the values of a and b.
\nSolution:<\/strong><\/span>
\n5x – 3 \u2264 5 + 3x \u2264\u00a04x + 2
\n5x – 3 \u2264\u00a05 + 3x and 5 + 3x \u2264 4x + 2
\n2x \u2264 8 and -x \u2264 -3
\nx \u2264 4 and x \u2265 3
\nThus, 3 \u2264 \u00a0x \u2264 4.
\nHence, a = 3 and b = 4.<\/p>\n

Question 11.<\/strong><\/span>
\nSolve the following inequation and graph the solution set on the number line:
\n2x – 3 < x + 2 \u2264 3x + 5, x \u2208 R.
\nSolution:<\/strong><\/span>
\n2x – 3 < x + 2 \u2264\u00a03x + 5
\n2x – 3 < x + 2 and x + 2 \u2264 3x + 5
\nx < 5 and -3 \u2264\u00a02x
\nx < 5 and -1.5 \u2264 x
\nSolution set = {-1.5 \u2264 x < 5}
\nThe solution set can be graphed on the number line as:
\n\"Selina<\/p>\n

Question 12.<\/strong><\/span>
\nSolve and graph the solution set of:
\n(i) 2x – 9 < 7 and 3x + 9 \u2264 25, x \u2208 R (ii) 2x – 9 \u2264 7 and 3x + 9 > 25, x \u2208 I
\n(iii) x + 5 \u2265 4(x – 1) and 3 – 2x < -7, x \u2208 R
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 13.<\/strong><\/span>
\nSolve and graph the solution set of:
\n(i) 3x – 2 > 19 or 3 – 2x \u2265 -7, x \u2208 R
\n(ii) 5 > p – 1 > 2 or 7 \u2264 2p – 1 \u2264 17, p \u2208 R
\nSolution:<\/strong><\/span>
\n(i) 3x – 2 > 19 or 3 – 2x \u2265\u00a0-7
\n3x > 21 or -2x \u2265\u00a0-10
\nx > 7 or x \u2264 5
\nGraph of solution set of x > 7 or x \u2264\u00a05 = Graph of points which belong to x > 7 or x \u2264\u00a05 or both.
\nThus, the graph of the solution set is:
\n\"Selina
\n(ii) 5 > p – 1 > 2 or 7 \u2264\u00a02p – 1 \u2264\u00a017
\n6 > p > 3 or 8 \u2264 2p \u2264\u00a018
\n6 > p > 3 or 4 \u2264 p \u2264\u00a09
\nGraph of solution set of 6 > p > 3 or 4 \u2264 p \u2264 9
\n= Graph of points which belong to 6 > p > 3 or 4 \u2264 p \u2264 9 or both
\n= Graph of points which belong to 3 < p \u2264\u00a09
\nThus, the graph of the solution set is:
\n\"Selina<\/p>\n

Question 14.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n(i) A = {x \u2208\u00a0R: -2 \u2264\u00a0x < 5}
\nB = {x \u2208\u00a0R: -4 \u2264 x < 3}
\n(ii) A \u2229\u00a0B = {x \u2208 R: -2 \u2264 x < 5}
\nIt can be represented on number line as:
\n\"Selina
\nB’ = {x \u2208\u00a0R: 3 < x \u2264 -4}
\nA \u2229\u00a0B’ = {x \u2208\u00a0R: 3 \u2264\u00a0x < 5}
\nIt can be represented on number line as:
\n\"Selina<\/p>\n

Question 15.<\/strong><\/span>
\nUse real number line to find the range of values of x for which:
\n(i) x > 3 and 0 < x < 6
\n(ii) x < 0 and -3 \u2264 x < 1
\n(iii) -1 < x \u2264 6 and -2 \u2264 x \u2264 3
\nSolution:<\/strong><\/span>
\n(i) x > 3 and 0 < x < 6
\nBoth the given inequations are true in the range where their graphs on the real number lines overlap.
\nThe graphs of the given inequations can be drawn as:
\n\"Selina
\nFrom both graphs, it is clear that their common range is
\n3 < x < 6
\n(ii) x < 0 and -3 \u2264\u00a0x < 1
\nBoth the given inequations are true in the range where their graphs on the real number lines overlap.
\nThe graphs of the given inequations can be drawn as:
\n\"Selina
\nFrom both graphs, it is clear that their common range is
\n-3 \u2264\u00a0x < 0
\n(iii) -1 < x \u2264 6 and -2 \u2264 x \u2264 3
\nBoth the given inequations are true in the range where their graphs on the real number lines overlap.
\nThe graphs of the given inequations can be drawn as:
\n\"Selina
\nFrom both graphs, it is clear that their common range is
\n-1 < x \u2264 3<\/p>\n

Question 16.<\/strong><\/span>
\nIllustrate the set {x: -3 \u2264 x < 0 or x > 2, x \u2208 R} on the real number line.
\nSolution:<\/strong><\/span>
\nGraph of solution set of -3 \u2264 x < 0 or x > 2
\n= Graph of points which belong to -3 \u2264 x < 0 or x > 2 or both
\nThus, the required graph is:
\n\"Selina<\/p>\n

Question 17.<\/strong><\/span>
\nGiven A = {x: -1 < x \u2264 5, x \u2208 R} and B = {x: -4 \u2264 x < 3, x \u2208 R}
\nRepresent on different number lines:
\n(i) A \u2229 B
\n(ii) A’ \u2229 B
\n(iii) A – B
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 18.<\/strong><\/span>
\nP is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 \u2265 5(x – 5); where x \u2208 R. Represent:
\n(i) P \u2229 Q
\n(ii) P – Q
\n(iii) P \u2229 Q’
\non different number lines.
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 19.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 20.<\/strong><\/span>
\nGiven: A = {x: -8 < 5x + 2 \u2264 17, x \u2208 I}, B = {x: -2 \u2264 7 + 3x < 17, x \u2208 R}
\nWhere R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A \u2229 B.
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 21.<\/strong><\/span>
\nSolve the following inequation and represent the solution set on the number line 2x – 5 \u2264 5x +4 < 11, where x \u2208 I
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 22.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 23.<\/strong><\/span>
\nGiven:
\nA = {x: 11x – 5 > 7x + 3, x \u2208 R} and
\nB = {x: 18x – 9 \u2265 15 + 12x, x \u2208 R}.
\nFind the range of set A \u2229 B and represent it on number line.
\nSolution:<\/strong><\/span>
\nA = {x: 11x – 5 > 7x + 3, x \u2208\u00a0R}
\n= {x: 4x > 8, x \u2208\u00a0R}
\n= {x: x > 2, x \u2208\u00a0R}
\nB = {x: 18x – 9 \u2265\u00a015 + 12x, x \u2208\u00a0R}
\n= {x: 6x \u2265\u00a024, x \u2208\u00a0R}
\n= {x: x \u2265\u00a04, x \u2208 R}
\nA \u2229\u00a0B = {x: x \u2265\u00a04, x \u2208 R}
\nIt can be represented on number line as:
\n\"Selina<\/p>\n

Question 24.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 25.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 26.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 27.<\/strong><\/span>
\nFind three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is atmost 20.
\nSolution:<\/strong><\/span>
\nLet the required integers be x, x + 1 and x + 2.
\nAccording to the given statement,
\n\"Selina
\nThus, the largest value of the positive integer x is 24.
\nHence, the required integers are 24, 25 and 26.<\/p>\n

Question 28.<\/strong><\/span>
\nSolve the given inequation and graph the solution on the number line.
\n2y – 3 < y + 1 \u2264 4y + 7, y \u2208\u00a0R
\nSolution:<\/strong><\/span>
\n2y – 3 < y + 1 \u2264 4y + 7, y \u2208\u00a0R
\n\u21d2 2y – 3 – y < y + 1 – y \u2264\u00a04y + 7 – y
\n\u21d2 y – 3 < 1 \u2264\u00a03y + 7
\n\u21d2 y – 3 < 1 and 1 \u2264\u00a03y + 7
\n\u21d2 y < 4 and 3y \u2265 6 \u21d2\u00a0y \u2265 – 2
\n\u21d2 – 2 \u2264\u00a0y < 4
\nThe graph of the given equation can be represented on a number line as:
\n\"Selina<\/p>\n

Question 29.<\/strong><\/span>
\nSolve the inequation:
\n3z – 5 \u2264 z + 3 < 5z – 9, z \u2208 R.
\nGraph the solution set on the number line.
\nSolution:<\/strong><\/span>
\n3z – 5 \u2264\u00a0z + 3 < 5z – 9
\n3z – 5 \u2264\u00a0z + 3 and z + 3 < 5z – 9
\n2z \u2264 8 and 12 < 4z
\nz \u2264 4 and 3 < z
\nSince, z R
\n\u2234 Solution set = {3 < z \u2264 4, x \u2208\u00a0R }
\nIt can be represented on a number line as:
\n\"Selina<\/p>\n

Question 30.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 31.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina<\/p>\n

Question 32.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 33.<\/strong><\/span>
\n\"Selina
\nSolution:<\/strong><\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 34.<\/strong><\/span>
\nSolve the following in equation and write the solution set:
\n13x – 5 < 15x + 4 < 7x + 12, x \u2208 R
\nSolution:<\/strong><\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 35.<\/strong><\/span>
\nSolve the following inequation, write the solution set and represent it on the number line.
\n-3(x – 7) \u2265 15 – 7x > x+1\/3, x R.
\nSolution:
\n<\/strong><\/span>\"Selina<\/p>\n

Question 36.
\n<\/strong><\/span>Solve the following inequation and represent the solution set on a number line.
\n\"Selina
\nSolution:
\n\"Selina
\n<\/strong><\/span><\/p>\n

More Resources for Selina Concise Class 10 ICSE Solutions<\/strong><\/p>\n