Question

solve the inequality and graph the solution on the line provided.
$-9 + 7x < 47$
answer attempt 1 out of 5
inequality notation:
number line:
number line from -12 to 12 with tick marks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12
touch and drag to plot line.
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Explanation:

Step1: Add 9 to both sides

To isolate the term with \( x \), we add 9 to both sides of the inequality \(-9 + 7x < 47\). This gives us \(-9 + 9 + 7x < 47 + 9\), 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, \(\frac{7x}{7} < \frac{56}{7}\), which simplifies to \(x < 8\).

Answer:

Inequality Notation: \( x < 8 \)
For the number line: Draw an open circle at 8 (since the inequality is strict, \( x < 8 \) not \( x \leq 8 \)) and shade the line to the left of 8 to represent all values of \( x \) less than 8.