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

Solve: | 2 x − 4 | < 3 Give your answer using interval notation.-example-1

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Solution

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))

User Olly F
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