Question

solve for ( x ) and graph the solution on the number line below. ( 26 < 5x + 6 ) and ( 66 > 5x + 6 )

Explanation:

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

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

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

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

Step3: Combine the two solutions

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

Answer:

The solution for \(x\) is \(4 < x < 12\). To graph this on a number line, draw an open circle at 4 and an open circle at 12, then shade the region between them.