Question

question
solve the inequality and graph the solution on the line provided.
5 + 7x < -51
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line
submit answer

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 \( 5 + 7x - 5 < -51 - 5 \), which simplifies to \( 7x < -56 \).

Step2: Divide both sides 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, \( \frac{7x}{7} < \frac{-56}{7} \), which simplifies to \( x < -8 \).

Answer:

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