3≤ 4 7x2≤ 2 ⇒ 3≤ 8 7x2≤ 2 ⇒ 6≤ 8 7x≤ 4 ⇒ 6≥ 7x 8≥ 4 ⇒ 6+8≥ 7x≥ 4+8 ⇒ 14≥ 7x≥ 4 ⇒ 4≤ 7x≤ 14 ⇒ 47≤ x≤ 2 ∴ x∈[47, ...

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Quadratic Formula

Solve: -3≤ 4...

Question

Solve: $- 3 \leq 4 - \frac{7 x}{2} \leq 2$

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Solution

$- 3 \leq 4 - \frac{7 x}{2} \leq 2$
$\Rightarrow - 3 \leq \frac{8 - 7 x}{2} \leq 2$
$\Rightarrow - 6 \leq 8 - 7 x \leq 4$
$\Rightarrow 6 \geq 7 x - 8 \geq - 4$
$\Rightarrow 6 + 8 \geq 7 x \geq - 4 + 8$
$\Rightarrow 14 \geq 7 x \geq 4$
$\Rightarrow 4 \leq 7 x \leq 14$
$\Rightarrow \frac{4}{7} \leq x \leq 2$
$∴ x \in [\frac{4}{7}, 2]$

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