Question

Solve: | 2 x − 4 | < 3 Give your answer using interval notation.

Answer 1

Given the expression below

`|2x-4|<3`

To find the values of x, we apply the absolute rule which is

`\begin{gathered} If\text{ \mid x\mid}0,\text{ then} \\ -aThen,<p>Where a = 3</p>[tex]-3<2x-4<3`

Then we solve separately,

For the first part

`-3<2x-4`

Solve for x

`\begin{gathered} Collect\text{ like terms} \\ -3+4<2x \\ 1<2x \\ Divde\text{ both sides by 2} \\ (1)/(2)<(2x)/(2) \\ (1)/(2)(1)/(2) \end{gathered}`

For the second part

`2x-4<3`

Solve for x

`\begin{gathered} Collect\text{ like terms} \\ 2x<3+4 \\ 2x<7 \\ Divide\text{ both sides by 2} \\ (2x)/(2)<(7)/(2) \\ x<(7)/(2) \end{gathered}`
`(1)/(2)<p><strong>Hence, the answer in interval notation is</strong></p>[tex]((1)/(2),(7)/(2))`