Question

solve for x and graph the solution on the number line below. 26 < 5x + 6 and 66 > 5x + 6 answer attempt 1 out of 160 inequality notation: number line: click and drag to plot line. -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

Step1: Solve the first inequality \(26 < 5x + 6\)

Subtract 6 from both sides: \(26 - 6 < 5x\)
\(20 < 5x\)
Divide both sides by 5: \(\frac{20}{5} < x\)
\(4 < x\)

Step2: Solve the second inequality \(66 > 5x + 6\)

Subtract 6 from both sides: \(66 - 6 > 5x\)
\(60 > 5x\)
Divide both sides by 5: \(\frac{60}{5} > x\)
\(12 > x\)

Step3: Combine the two inequalities

From Step1, \(x > 4\); from Step2, \(x < 12\). So the solution is \(4 < x < 12\)

Answer:

Inequality Notation: \(4 < x < 12\)
For the number line: Plot an open circle at 4 and 12, then draw a line segment between them (since \(x\) is greater than 4 and less than 12, not including 4 and 12).