Solve |2x-9|<7A. [xlx<1 or x>8}B. {x11C. xl-1

Question

Solve B. {x11C. {xl-1

Answer 1

Given the inequality:

`|2x-9|\lt7`

This is equivalent to:

`-7\lt2x-9\lt7`

We add 9 on each side of the inequality:

`\begin{gathered} -7+9\lt2x-9+9\lt7+9 \\ 2\lt2x\lt16 \end{gathered}`

Now, we divide by two:

`\begin{gathered} (2)/(2)\lt(2x)/(2)\lt(16)/(2) \\ \\ 1\lt x\lt8 \end{gathered}`

The answer is:

`\lbrace x|x\gt1\text{ or }x\lt8\rbrace`