Question

Solve the following inequality. Write the solution set in interval notation, and graph it.-21 ≤5x-9≤1The solution set is _____(Type your answer in interval notation. Type an integer or a simplified fraction.)

Answer 1

The inequality is given to be:

$-21\:\le 5x-9\le 1$

Recall the inequality rule:

$\mathrm{If}\:a\le \:u\le \:b\:\mathrm{then}\:a\le \:u\quad \mathrm{and}\quad \:u\le \:b$

Therefore, we have that:

$-21\le \:5x-9\quad \mathrm{and}\quad \:5x-9\le \:1$

Solving each inequality individually, we have:

$\begin{gathered} -21\leq5x-9 \\ -21+9\leq5x \\ -12\leq5x \\ \therefore \\ -\frac{12}{5}\leq x \end{gathered}$

and

$\begin{gathered} 5x-9\leq1 \\ 5x\leq1+9 \\ 5x\leq10 \\ \therefore \\ x\leq\frac{10}{5} \\ x\leq2 \end{gathered}$

Therefore, the solution set is:

$-\frac{12}{5}\leq x\leq2$

The graph is shown below: