Question

solve the inequality and graph the solution on the line provided.
-6x + 2 > 32
answer attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( x \), we subtract 2 from both sides of the inequality \( -6x + 2 > 32 \). This gives us \( -6x + 2 - 2 > 32 - 2 \), which simplifies to \( -6x > 30 \).

Step2: Divide by -6 and reverse inequality

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -6x > 30 \) by -6, we get \( x < \frac{30}{-6} \), which simplifies to \( x < -5 \).

Answer:

Inequality Notation: \( x < -5 \)
For the number line: Plot an open circle at -5 (since the inequality is strict, \( x < -5 \) not \( x \leq -5 \)) and draw an arrow to the left of -5 to represent all values less than -5.