Question

Solve the compound inequality. Graph the solution set. 5x-2<13 and -6x+2>-18

Answer 1

Given the first inequality,

`5x-2<13`

Let us solve for x,

`\begin{gathered} \text{collect like terms,} \\ 5x<13+2 \\ 5x<15 \\ \text{divide both sides by 5} \\ (5x)/(5)<(15)/(5) \\ x<3 \end{gathered}`

Given the second inequality,

`\begin{gathered} -6x+2>-28 \\ \text{collect like terms,} \\ -6x>0-28-2 \end{gathered}`
`\begin{gathered} -6x>-30 \\ \text{divide both sides -6} \\ (-6x)/(-6)<(-30)/(-6) \\ x<5 \end{gathered}`

The solutions for x for the two inequalities are,

`\begin{gathered} x<3,\text{ and} \\ x<5 \end{gathered}`

Hence, we have

`(-\infty,3)\cap(-\infty,5)=(-\infty,3)`

Hence, the solution is the interval (-∞, 3)