Question

Solve the compound inequality. 4x+15 ≥-9 and 8x-6 ≤ 34

Answer 1

Solution :

Given, compound inequality, $4x+15 \geq - 9$ and $8x-6 \leq 34$ .

Let us solve the first inequality for x

$4x+15 \geq - 9\\\Rightarrow 4x\geq -9-15\\\Rightarrow 4x\geq -24\\\Rightarrow x\geq\frac{-24}{4} \\\Rightarrow x\geq -6$

Now, on solving the second inequality for x, we get

$8x-6\leq 34\\ => 8x\leq 34 +6\\=> 8x\leq 40\\=> x\leq \frac{40}{8} \\=> x\leq 5$

Hence, the Solution of compound inequality can be expressed as $-6 \leq x\leq 5$

Answer 2

For the first one x>-6, for the second one x< or equal to 5