Question

solve for x.
-17 ≤ x - 6 + 10x < -6
write your answer as a compound inequality with integers.

Explanation:

Step1: Combine like - terms

Combine $x$ and $10x$ in the compound - inequality $-17\leq x - 6+10x\lt - 6$. We get $-17\leq11x - 6\lt - 6$.

Step2: Add 6 to all parts

Adding 6 to each part of the compound - inequality $-17\leq11x - 6\lt - 6$ gives $-17 + 6\leq11x-6 + 6\lt - 6+6$, which simplifies to $-11\leq11x\lt0$.

Step3: Divide all parts by 11

Dividing each part of the compound - inequality $-11\leq11x\lt0$ by 11, we have $\frac{-11}{11}\leq\frac{11x}{11}\lt\frac{0}{11}$, so $-1\leq x\lt0$.

Answer:

$-1\leq x\lt0$