Question

Solve for x:18x − 5 < −8 or 7x − 4 ≥ 38Enter your answer, including the inequality symbol, in the boxes.

Answer 1

`(-\infty,-(1)/(6))\cup[6,\infty)`

Step-by-step explanation

We want to solve the inequality:

`18x-5<-8\text{ or }7x-4\ge38`

Let us solve the first inequality.

First, add 5 to both sides of the inequality:

`\begin{gathered} 18x-5+5<-8+5 \\ \\ 18x<-3 \end{gathered}`

Now, divide both sides of the inequality by 18:

`\begin{gathered} x<(-3)/(18) \\ \\ x<-(1)/(6) \end{gathered}`

Let us solve the second inequality. Add 4 to both sides of the inequality:

`\begin{gathered} 7x-4+4\ge38+4 \\ \\ 7x\ge42 \end{gathered}`

Now, divide both sides of the inequality by 7:

`\begin{gathered} x\ge(42)/(7) \\ \\ x\ge6 \end{gathered}`

Therefore, the solution for x is:

`\begin{gathered} x<-(1)/(6)\text{ or }x\ge6 \\ \\ (-\infty,-(1)/(6))\cup[6,\infty) \end{gathered}`