Question

solve the inequality and graph the solution on the line provided.
-4x - 46 < -38
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
(number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked, and instructions to click and drag to plot lines.)
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Explanation:

Step1: Add 46 to both sides

To isolate the term with \( x \), we add 46 to both sides of the inequality \( -4x - 46 < -38 \). This gives us \( -4x - 46 + 46 < -38 + 46 \), which simplifies to \( -4x < 8 \).

Step2: Divide by -4 (reverse inequality)

When dividing both sides of an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \( -4x < 8 \) by -4, we get \( \frac{-4x}{-4} > \frac{8}{-4} \), which simplifies to \( x > -2 \).

Answer:

Inequality Notation: \( x > -2 \)
For the number line: We would draw an open circle at -2 (since the inequality is strict, \( > \), not \( \geq \)) and shade the region to the right of -2 to represent all values of \( x \) greater than -2.