Question

solve the inequality and graph the solution on the line provided.
$7x + 32 < 67$
answer attempt 1 out of 2
inequality notation:
number line:
(number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12)

Explanation:

Step1: Subtract 32 from both sides

To isolate the term with \( x \), we subtract 32 from both sides of the inequality \( 7x + 32 < 67 \). This gives us \( 7x + 32 - 32 < 67 - 32 \), which simplifies to \( 7x < 35 \).

Step2: Divide both sides by 7

To solve for \( x \), we divide both sides of the inequality \( 7x < 35 \) by 7. This gives us \( \frac{7x}{7} < \frac{35}{7} \), which simplifies to \( x < 5 \).

Answer:

Inequality Notation: \( x < 5 \)
For the number line: We draw an open circle at 5 (since \( x \) is less than 5, not less than or equal to 5) and shade the region to the left of 5 to represent all values of \( x \) that satisfy the inequality.