Question

solve the inequality and graph the solution on the line provided.
$5 + 7x < -51$
answer attempt 3 out of 3
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 5 from both sides

To isolate the term with \( x \), we subtract 5 from both sides of the inequality \( 5 + 7x < -51 \). This gives us \( 7x < -51 - 5 \), which simplifies to \( 7x < -56 \).

Step2: Divide by 7

Next, we divide both sides of the inequality \( 7x < -56 \) by 7. Since 7 is a positive number, the direction of the inequality sign remains the same. So we have \( x < \frac{-56}{7} \), which simplifies to \( x < -8 \).

Answer:

Inequality Notation: \( x < -8 \)
For the number line: We place an open circle at -8 (because the inequality is strict, \( < \), not \( \leq \)) and draw a line to the left of -8 to represent all values of \( x \) less than -8.