Question

solve the inequality and graph the solution on the line provided.
8 + 3x > 23
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.
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Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( x \), we subtract 8 from both sides of the inequality \( 8 + 3x > 23 \). This gives us \( 3x > 23 - 8 \). Calculating the right - hand side, \( 23-8 = 15 \), so the inequality becomes \( 3x>15 \).

Step2: Divide both sides by 3

To solve for \( x \), we divide both sides of the inequality \( 3x > 15 \) by 3. Since 3 is a positive number, the direction of the inequality sign remains the same. So we have \( \frac{3x}{3}>\frac{15}{3} \), which simplifies to \( x > 5 \).

For the number line graph: We draw an open circle at \( x = 5 \) (because the inequality is \( x>5 \), not \( x\geq5 \)) and then draw an arrow to the right of 5 to represent all the numbers greater than 5.

Answer:

Inequality Notation: \( x > 5 \)
(For the number line: Open circle at 5, arrow pointing to the right)