Question

solve the inequality and graph the solution on the line provided.
-13 + 8x ≤ -45
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
submit answer

Explanation:

Step1: Isolate the term with \(x\)

Add \(13\) to both sides of the inequality \(-13 + 8x\leq -45\).
Using the addition property of inequalities (\(a + c\leq b + c\) if \(a\leq b\)), we get \(-13+13 + 8x\leq -45 + 13\).
Simplify to \(8x\leq-32\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(8x\leq -32\) by \(8\).
Using the division property of inequalities (\(\frac{a}{c}\leq\frac{b}{c}\) for \(c>0\)), we have \(\frac{8x}{8}\leq\frac{-32}{8}\).
Simplify to \(x\leq - 4\).

Answer:

Inequality Notation: \(x\leq - 4\)

To graph on the number - line: Place a closed circle at \(-4\) (because the inequality is \(\leq\)) and shade to the left of \(-4\) (since \(x\) is less than or equal to \(-4\)).