How do you solve and check for extraneous solutions in $abs(2x + 3) = 5$ ?

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How do you solve and check for extraneous solutions in $abs(2x + 3) = 5$ ?

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Answer 1 · 2015-08-01T12:53:56

Solve: |2x + 3| = 5

Ans : x = 1, x = - 4

Explanation:

separate solving in 2 cases:
a. (2x + 3) = 5 --> 2x = 2 --> $x = 1$

b. - (2x + 3 ) = 5 --> -2x - 3 = 5 --> -2x = 8 --> $x = - 4$

Answer 2 · 2015-08-01T14:57:29

$color(red)(x = 1)$ and $color(red)(x = -4)$ .
There are $color(red)(" no")$ extraneous solutions.

Explanation:

SOLVE

We need to write two different equations without the absolute value symbols and solve for $x$ .

These equations are
(1): $(2x+3) = 5$
(2): $-(2x+3) = 5$

Solve Equation 1:

$2x+3 = 5$

Subtract $3$ from each side.

$2x = 2$

Divide each side by $2$ .

$x = 1$

Solve Equation 2:

$−(2x+3) = 5$

Remove parentheses.

$−2x−3= 5$

Add $3$ to each side.

$-2x = 8$

Divide each side by $-2$ .

$x = -4$

The solutions are $x = 0$ and $x = -4$ .

CHECK FOR EXTRANEOUS SOLUTIONS:

If $x = 1$ ,

$|2x+3|=5$
$|2×1+3|= 5$
$|2+3| = 5$
$|5| =5$
$5=5$

$x=1$ is a true solution.

If $x= -4$ ,

$|2x+3|=5$
$|2(-4) + 3| = 5$
$|-8 + 3| = 5$
$|-5| = 5$
$5 = 5$

$x=5$ is a true solution.

There are no extraneous solutions.

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How do you solve and check for extraneous solutions in $abs(2x + 3) = 5$ ?

2 Answers

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Science

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How do you solve and check for extraneous solutions in abs(2x + 3) = 5abs(2x + 3) = 5?

2 Answers

Explanation:

Explanation:

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How do you solve and check for extraneous solutions in $abs(2x + 3) = 5$ ?