Question

an inequality is shown. 7x + 10 - 11x ≤ 2. solve the inequality and graph the solution on the number line.

Explanation:

Step1: Combine like - terms

$7x+10 - 11x\leq2$ simplifies to $(7x-11x)+10\leq2$, which is $- 4x+10\leq2$.

Step2: Subtract 10 from both sides

$-4x+10 - 10\leq2 - 10$, resulting in $-4x\leq - 8$.

Step3: Divide both sides by - 4 and reverse the inequality sign

Since we are dividing by a negative number, when we divide $-4x\leq - 8$ by $-4$, we get $x\geq2$.

To graph on the number line, we draw a closed circle at 2 (because the inequality is $\geq$) and draw an arrow to the right.

Answer:

The solution of the inequality is $x\geq2$. On the number - line, there is a closed circle at 2 and an arrow pointing to the right.