Question

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank.
19 < 2x + 5 and 2x + 5 < 27
answer attempt 1 out of 4
inequality notation:
number line:
(there is a number line with -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked and a click and drag to plot line instruction)
submit answer

Explanation:

Step1: Solve the first inequality

We have \(19 < 2x + 5\). Subtract 5 from both sides: \(19 - 5<2x + 5 - 5\), which simplifies to \(14 < 2x\). Then divide both sides by 2: \(\frac{14}{2}<\frac{2x}{2}\), so \(7 < x\).

Step2: Solve the second inequality

We have \(2x + 5 < 27\). Subtract 5 from both sides: \(2x+5 - 5<27 - 5\), which simplifies to \(2x < 22\). Then divide both sides by 2: \(\frac{2x}{2}<\frac{22}{2}\), so \(x < 11\).

Step3: Combine the inequalities

Since we have \(7 < x\) and \(x < 11\), we can write this as a single inequality \(7 < x < 11\).

Answer:

The inequality notation is \(7 < x < 11\). For the number line, we would plot an open circle at 7 and an open circle at 11, and shade the region between them.