Question

compound inequalities (l2)
score: 1/5 penalty: 1 off
question
solve for $x$ and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution ($\varnothing$), leave the number line blank.
$-5x + 6 \leq 26$ and $-5x + 6 \geq -24$
inequality notation:

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of $-5x + 6\leqslant26$:
$-5x+6 - 6\leqslant26 - 6$, which simplifies to $-5x\leqslant20$.
Divide both sides by - 5, and reverse the inequality sign: $x\geqslant - 4$.

Step2: Solve the second inequality

Subtract 6 from both sides of $-5x + 6\geqslant - 24$:
$-5x+6 - 6\geqslant - 24 - 6$, which simplifies to $-5x\geqslant - 30$.
Divide both sides by - 5, and reverse the inequality sign: $x\leqslant6$.

Answer:

$-4\leqslant x\leqslant6$