Question

solve for x and graph the solution on the number line below. 6 > 4x - 6 or 4x - 6 > 22 answer attempt 1 out of 2 inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 click and drag to plot line.

Explanation:

Step1: Solve \( 6 > 4x - 6 \)

Add 6 to both sides: \( 6 + 6 > 4x - 6 + 6 \)
Simplify: \( 12 > 4x \)
Divide by 4: \( \frac{12}{4} > \frac{4x}{4} \)
Simplify: \( 3 > x \) or \( x < 3 \)

Step2: Solve \( 4x - 6 > 22 \)

Add 6 to both sides: \( 4x - 6 + 6 > 22 + 6 \)
Simplify: \( 4x > 28 \)
Divide by 4: \( \frac{4x}{4} > \frac{28}{4} \)
Simplify: \( x > 7 \)

Step3: Combine the solutions

Since it's an "or" statement, the solution is \( x < 3 \) or \( x > 7 \)

Answer:

Inequality Notation: \( x < 3 \) or \( x > 7 \)

For the number line: Plot an open circle at 3 and shade to the left, and plot an open circle at 7 and shade to the right.