Question

question 13
the inequality 2x + 10 ≤ x + 7 ≤ 3x + 16 means that x is in the closed interval a, b where
a is:
and b is:
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Explanation:

Step1: Split the compound - inequality

We split $2x + 10\leq x + 7\leq3x+16$ into two inequalities: $2x + 10\leq x + 7$ and $x + 7\leq3x+16$.

Step2: Solve $2x + 10\leq x + 7$

Subtract $x$ from both sides: $2x - x+10\leq x - x + 7$, which simplifies to $x+10\leq7$. Then subtract 10 from both sides: $x\leq7 - 10$, so $x\leq - 3$.

Step3: Solve $x + 7\leq3x+16$

Subtract $x$ from both sides: $x - x+7\leq3x - x+16$, which gives $7\leq2x + 16$. Then subtract 16 from both sides: $7-16\leq2x+16 - 16$, so $-9\leq2x$. Divide both sides by 2: $x\geq-\frac{9}{2}=-4.5$.

Answer:

$A=-4.5$
$B = - 3$