Question

solve for x and graph the solution on the number line below.
58 ≥ 5x + 3 > -42

Explanation:

Step1: Subtract 3 from all parts

To solve the compound inequality \( 58 \geq 5x + 3 > -42 \), we first subtract 3 from each part. This gives us \( 58 - 3 \geq 5x + 3 - 3 > -42 - 3 \), which simplifies to \( 55 \geq 5x > -45 \).

Step2: Divide all parts by 5

Next, we divide each part of the inequality by 5. So, \( \frac{55}{5} \geq \frac{5x}{5} > \frac{-45}{5} \), which simplifies to \( 11 \geq x > -9 \). In inequality notation, this can be written as \( -9 < x \leq 11 \).

Answer:

The solution in inequality notation is \( -9 < x \leq 11 \). For the number line graph, we would have an open circle at -9 (since \( x > -9 \)) and a closed circle at 11 (since \( x \leq 11 \)), with a line segment connecting them.