Additional Mathematics – Equations, inequalities and graphs | e-Consult
Equations, inequalities and graphs (1 questions)
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Both sides are non‑negative, so square the inequality:
16(x + 1)² ≤ (3x − 2)²
Expand:
- 16(x² + 2x + 1) ≤ 9x² − 12x + 4
- 16x² + 32x + 16 ≤ 9x² − 12x + 4
- 7x² + 44x + 12 ≤ 0
Find the roots of 7x² + 44x + 12 = 0:
Δ = 44² − 4·7·12 = 1600, √Δ = 40
x = [−44 ± 40]/(2·7) ⟹ x₁ = −6, x₂ = −2⁄7
Since the quadratic opens upwards, it is ≤ 0 between the roots:
| [−6, −2⁄7] |
Thus the solution set is −6 ≤ x ≤ −2⁄7.