Question

question
solve the inequality and graph the solution on the line provided.
83 - 7x ≥ 111
answer attempt 1 out of 5
≤ > < ≥ or
inequality notation:
number line:

Explanation:

Step1: Subtract 83 from both sides

To isolate the term with \( x \), we subtract 83 from both sides of the inequality \( 83 - 7x \geq 111 \). This gives us:
\( 83 - 83 - 7x \geq 111 - 83 \)
Simplifying both sides, we get:
\( -7x \geq 28 \)

Step2: Divide by -7 (and reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. So we divide both sides of \( -7x \geq 28 \) by -7:
\( \frac{-7x}{-7} \leq \frac{28}{-7} \)
Simplifying, we find:
\( x \leq -4 \)

Answer:

Inequality Notation: \( x \leq -4 \)
(For the number line graph, we would draw a closed circle at -4 and shade to the left of -4, indicating all values less than or equal to -4.)