How do you solve and graph $| 2 x + 1 | > - 3$ $|2x + 1| > -3$ ?

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How do you solve and graph $| 2 x + 1 | > - 3$ $|2x + 1| > -3$ ?

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Answer 1 · 2018-03-10T04:59:52

$x > - 2 or x < 1$ $x> -2 or x <1$

Explanation:

$| 2 x + 1 | > - 3$ $|2x +1| > -3$

Solve for the absolute value

We know either: $2 x + 1 > - 3 or 2 x + 1 < - (- 3)$ $2x+1> -3 or 2x + 1 < - (-3)$

Now let's solve the first possibility which is $2 x + 1 > - 3$ $2x + 1 > -3$

$2 x + 1 > - 3$ $2x + 1 > -3$

Add $- 1$ $-1$ on both sides

$2 x + 1 - 1 > - 3 - 1$ $2x + 1 -1 > -3 - 1$

$2 x > - 4$ $2x > -4$

Divide both sides by $2$ $2$

$\frac{2 x}{2} > \frac{- 4}{2}$ $(2x)/2 > (-4)/2$

$x > - 2$ $x > -2$

Now let's solve the second possibility

$2 x + 1 < - (- 3)$ $2x + 1 < - (-3)$

$2 x + 1 < 3$ $2x + 1< 3$

Add $- 1$ $-1$ on both sides

$2 x + 1 - 1 < 3 - 1$ $2x + 1 - 1 < 3 -1$

$2 x < 2$ $2x < 2$

$\frac{2 x}{2} < \frac{2}{2}$ $(2x)/2 < 2/2$

$x < 1$ $x < 1$

Thus,

The answers are:

$x > - 2 or x < 1$ $x > -2 or x < 1$

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How do you solve and graph $| 2 x + 1 | > - 3$ $|2x + 1| > -3$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve and graph |2x+1|>−3 |2x + 1| > -3?

1 Answer

Explanation:

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How do you solve and graph $| 2 x + 1 | > - 3$ $|2x + 1| > -3$ ?