Question

Solve3x - 5<-14 or 2x - 1 > 7for x

Answer 1

x < -3 or x > 4

Step-by-step explanation

Because we have or connecting the two inequalities, we don't need both inequalities to be true at the same time. Therefore we can solve them separately.

Solve the first one:

`3x-5\lt-14`

Add 5 to both sides of the inequality:

`\begin{gathered} 3x-5+5\lt-14+5 \\ 3x\lt-9 \end{gathered}`

And divide both sides by 3:

`\begin{gathered} (3x)/(3)\lt-(9)/(3) \\ x\lt-3 \end{gathered}`

Solve the second inequality:

`2x-1>7`

Add 1 to both sides of the inequality:

`\begin{gathered} 2x-1+1>7+1 \\ 2x>8 \end{gathered}`

And divide both sides by 2:

`\begin{gathered} (2x)/(2)>(8)/(2) \\ x>4 \end{gathered}`

Hence the solution for x is x < -3 or x > 4.