Question

Solve: 2 (x − 3) – 7 (x + 5) ≤ 3x – 9 and (x + 5) – 7 (x – 2) ≥ 4x + 9, x ∈ R and represent the solution on the number line.

Answer 1

1) 2(x − 3) −7(x + 5) ≤ 3x − 9

2x − 6 − 7x − 35 ≤ 3x − 9

−5x − 41 ≤ 3x − 9

−8x ≤ 32

Divide by −8

x ≥ −4

2) (x + 5) −7(x − 2) ≥ 4x + 9

x + 5 − 7x + 14 ≥ 4x + 9

−6x + 19 ≥ 4x + 9

−10x ≥ −10

Divide by −10

x ≤ 1

x ≥ −4 and x ≤ 1

⇒ x ∈ [−4, 1]

−4 ≤ x ≤ 1

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