Question

1. solve the following inequality: 2(5x + 20) ≤ -20

15a solve the inequality.
x ≤ -6
15b now, plot the inequality 2(5x + 20) ≤ -20 on the number line below.

Explanation:

Step1: Expand the left - hand side

$2(5x + 20)=10x+40$, so the inequality becomes $10x + 40\leq - 20$.

Step2: Subtract 40 from both sides

$10x+40 - 40\leq - 20-40$, which simplifies to $10x\leq - 60$.

Step3: Divide both sides by 10

$\frac{10x}{10}\leq\frac{-60}{10}$, resulting in $x\leq - 6$.

For 15b:
On the number - line, we place a closed circle at $x = - 6$ (because the inequality is $\leq$) and shade the line to the left of $x=-6$ to represent all the values of $x$ that satisfy the inequality.

Answer:

15a: $x\leq - 6$
15b: Place a closed circle at $-6$ and shade to the left on the number - line.