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

Solution :Given, compound inequality, [tex] 4x+15 \geq - 9 [/tex] and [tex] 8x-6 \leq 34 [/tex] .Let us solve the first inequality for x[tex] 4x+15 \geq - 9\\\Rightarrow 4x\geq -9-15\\\Rightarrow 4x\geq -24\\\Rightarrow x\geq\frac{-24}{4} \\\Rightarrow x\geq -6 [/tex]Now, on solving the second inequality for x, we get[tex] 8x-6\leq 34\\ => 8x\leq 34 +6\\=> 8x\leq 40\\=> x\leq \frac{40}{8} \\=> x\leq 5 [/tex]Hence, the Solution of compound inequality can be expressed as [tex] -6 \leq x\leq 5 [/tex]