Question

solve the inequality and graph the solution set on a number line.
6x - 5 > -x + 16

Explanation:

Step1: Add \(x\) to both sides

To isolate the \(x\) terms, we add \(x\) to both sides of the inequality \(6x - 5 > -x + 16\). This gives us \(6x + x - 5 > -x + x + 16\), which simplifies to \(7x - 5 > 16\).

Step2: Add 5 to both sides

Next, we add 5 to both sides to isolate the term with \(x\). So, \(7x - 5 + 5 > 16 + 5\), which simplifies to \(7x > 21\).

Step3: Divide by 7

Finally, we divide both sides by 7 to solve for \(x\). \(\frac{7x}{7} > \frac{21}{7}\), which simplifies to \(x > 3\).

Answer:

The solution to the inequality \(6x - 5 > -x + 16\) is \(x > 3\). To graph this on a number line, we draw an open circle at 3 (since \(x\) is not equal to 3) and shade the region to the right of 3.