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.

$-5x - 3 \leq -48$ or $-5x - 3 > -63$

answer attempt 1 out of 2

inequality notation:

number line:

submit answer

Explanation:

Step1: Solve the first inequality

For \(-5x - 3\leq - 48\), add \(3\) to both sides:
\(-5x-3 + 3\leq -48 + 3\), so \(-5x\leq - 45\).
Divide both sides by \(-5\) (and reverse the inequality sign because we are dividing by a negative number):
\(x\geq\frac{-45}{-5}\), so \(x\geq9\).

Step2: Solve the second inequality

For \(-5x - 3> - 63\), add \(3\) to both sides:
\(-5x-3 + 3> - 63+3\), so \(-5x> - 60\).
Divide both sides by \(-5\) (and reverse the inequality sign):
\(x<\frac{-60}{-5}\), so \(x < 12\).

Answer:

The solution in inequality notation is \(9\leq x<12\). On the number - line, we have a closed circle at \(x = 9\) (because \(x\) can be equal to \(9\)) and an open circle at \(x = 12\) (because \(x\) cannot be equal to \(12\)) with a line segment connecting them.