Question

solve the inequality and graph the solution on the line provided.

$-6 + 6x \leq 24$

answer attempt 1 out of 2

$<$ $>$ $\leq$ $\geq$ or

inequality notation: \boxed{}

number line:

number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12

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Explanation:

Step1: Add 6 to both sides

To isolate the term with \(x\), we add 6 to both sides of the inequality \(-6 + 6x \leq 24\). This gives us \(-6 + 6 + 6x \leq 24 + 6\), which simplifies to \(6x \leq 30\).

Step2: Divide by 6

Next, we divide both sides of the inequality \(6x \leq 30\) by 6 to solve for \(x\). So, \(\frac{6x}{6} \leq \frac{30}{6}\), which simplifies to \(x \leq 5\).

Answer:

Inequality Notation: \(x \leq 5\)

For the number line: We place a closed circle at 5 (since the inequality is "less than or equal to") and shade to the left of 5 to represent all values of \(x\) that satisfy the inequality.