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Solve [tex]\( 4|x+5|=28 \)[/tex]

A. [tex]\( x=12 \)[/tex] and [tex]\( x=-2 \)[/tex]

B. [tex]\( x=-12 \)[/tex] and [tex]\( x=-2 \)[/tex]

C. [tex]\( x=12 \)[/tex] and [tex]\( x=-12 \)[/tex]

D. [tex]\( x=-12 \)[/tex] and [tex]\( x=2 \)[/tex]

Sagot :

GinnyAnsweridn
To solve the equation [tex]\( 4|x+5|=28 \)[/tex], let's follow a step-by-step approach.

1. Isolate the absolute value expression:
[tex]\[ 4|x+5| = 28 \][/tex]
Divide both sides by 4 to isolate the absolute value:
[tex]\[ |x+5| = 7 \][/tex]

2. Rewrite the absolute value equation:
The absolute value equation [tex]\( |x+5| = 7 \)[/tex] can be rewritten as two separate linear equations:
[tex]\[ x+5 = 7 \quad \text{or} \quad x+5 = -7 \][/tex]

3. Solve each linear equation:

- For [tex]\( x+5 = 7 \)[/tex]:
[tex]\[ x+5 = 7 \implies x = 7 - 5 \implies x = 2 \][/tex]

- For [tex]\( x+5 = -7 \)[/tex]:
[tex]\[ x+5 = -7 \implies x = -7 - 5 \implies x = -12 \][/tex]

4. List the solutions:
The solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].

Hence, the correct answer is:

D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]
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