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What is the solution set of |2x + 1| > 5?A. {x|1 < x <

–3} B. {x|–1 < x < 3} C. {x|x > 2 or x < –3} D. {x|x < 2

or x > –3}

2
by gerhgrehrttj

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–3} B. {x|–1 < x < 3} C. {x|x > 2 or x < –3} D. {x|x < 2

or x > –3}

by gerhgrehrttj

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Solution set is the set of all values of x, which satisfy the given condition.

| 2 x + 1 | > 5

Let a = | 2 x + 1 |

then a = 2 x + 1 if 2x+1 is positive or zero

= - 2x -1 if 2x+1 is negative of zero

Let 2x+1 be 0 or more.

so 2x + 1 > 5 => 2x > 5 - 1 = 4 => 2x > 4 => x > 2

Let 2x+1 be 0 or less

so - 2 x - 1 > 5 => -2 x > 6 => -x > 3 => x < -3

(as When you multiply by -1, the inequality reverses.)

__So we have x > 2 and x < -3.__

__Answer is option C__

There is also a quicker way:

|2x+1| > 5 => this is rewritten as

-5 > 2x+1 > 5 Left side gives, x < -3 & right side gives x >2

| 2 x + 1 | > 5

Let a = | 2 x + 1 |

then a = 2 x + 1 if 2x+1 is positive or zero

= - 2x -1 if 2x+1 is negative of zero

Let 2x+1 be 0 or more.

so 2x + 1 > 5 => 2x > 5 - 1 = 4 => 2x > 4 => x > 2

Let 2x+1 be 0 or less

so - 2 x - 1 > 5 => -2 x > 6 => -x > 3 => x < -3

(as When you multiply by -1, the inequality reverses.)

There is also a quicker way:

|2x+1| > 5 => this is rewritten as

-5 > 2x+1 > 5 Left side gives, x < -3 & right side gives x >2