If x ∈ Z-, find the solution set of each of the following inequations. Represent each solution set on the number line. (i) 3x - 14 (ii) -29 9x - 2 (iii) -4(x + 5) 9 (iv) 5 + 6x x - 10 (v) 10 - 2(1 + 4x) 26 (vi)

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(i) 3x - 14 We have: 3x - 14 ⇒ x ⇒ x -4.66... Negative integers greater than -4.66.. are {-4, -3, -2, -1} ∴ Solution set = {-4, -3, -2, -1} (ii) -29 9x - 2 We have: -29 9x - 2 ⇒ -29 + 2 9x [Adding 2 on both sides] ⇒ -27 9x ⇒ x [Dividing both sides by 9] ⇒ -3 x ⇒ x -3 Negative integers greater than -3 are {-2, -1} ∴ Solution set = {-2, -1} (iii) -4(x + 5) 9 We have: -4(x + 5) 9 ⇒ -4x - 20 9 ⇒ -4x 9 + 20 [Adding 20 on both sides] ⇒ -4x 29 ⇒ -x ⇒ -x 7.25 ⇒ x -7.25 [Multiplying -1 on both sides and reversing the sign] Negative integers greater than -7.25 are {-6, -5, -4, -3, -2, -1} ∴ Solution set = {-6, -5, -4, -3, -2, -1} (iv) 5 + 6x x - 10 We have: 5 + 6x x - 10 ⇒ 6x - x - 10 - 5 [Subtracting x and 5 from both sides] ⇒ 5x -15 ⇒ x ⇒ x -3 Negative integers greater than -3 are {-2, -1} ∴ Solution set = {-2, -1} (v) 10 - 2(1 + 4x) 26 We have: 10 - 2(1 + 4x) 26 ⇒ 10 - 2 - 8x 26 ⇒ 8 - 8x 26 ⇒ -8x 26 - 8 [Subtracting 8 from both sides] ⇒ -8x 18 ⇒ -x ⇒ -x 2.25 ⇒ x -2.25 [Multiplying -1 on both sides and reversing the sign] Negative integers greater than -2.25 are {-2, -1} ∴ Solution set = {-2, -1} (vi) We have: Negative integers less than -4.27... are {..., -6, -5} ∴ Solution set = {..., -6, -5}

Mathematics

If x ∈ Z-, find the solution set of each of the following inequations. Represent each solution set on the number line. (i) 3x - 14 (ii) -29 9x - 2 (iii) -4(x + 5) 9 (iv) 5 + 6x x - 10 (v) 10 - 2(1 + 4x) 26 (vi)

Linear Inequations

Related Questions

If a > b and m < 0, then which of the following is correct :
am < bm
am = bm
am > bm
am and bm cannot be compared

Mathematics

If x ∈ Z-, find the solution set of each of the following inequations. Represent each solution set on the number line. (i) 3x - 14 (ii) -29 9x - 2 (iii) -4(x + 5) 9 (iv) 5 + 6x x - 10 (v) 10 - 2(1 + 4x) 26 (vi)

Linear Inequations

Related Questions

If a > b and m < 0, then which of the following is correct :am < bmam = bmam > bmam and bm cannot be compared

If a > b and m < 0, then which of the following is correct :
am < bm
am = bm
am > bm
am and bm cannot be compared