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Which value of [tex]\( x \)[/tex] makes this equation true?

[tex]\[ -12x - 2(x + 9) = 5(x + 4) \][/tex]

A. [tex]\(-2\)[/tex]

B. [tex]\(5\)[/tex]

C. [tex]\(-\frac{1}{3}\)[/tex]

D. [tex]\(\frac{13}{19}\)[/tex]

Sagot :

GinnyAnsweridn
To determine which value of [tex]\( x \)[/tex] makes the equation true, let's solve the given equation step-by-step:

[tex]\[ -12x - 2(x + 9) = 5(x + 4) \][/tex]

First, distribute the constants inside the parentheses:

[tex]\[ -12x - 2 \cdot x - 2 \cdot 9 = 5 \cdot x + 5 \cdot 4 \][/tex]

Simplify the expression:

[tex]\[ -12x - 2x - 18 = 5x + 20 \][/tex]

Combine the like terms on the left side:

[tex]\[ -14x - 18 = 5x + 20 \][/tex]

Next, we want to get all the terms involving [tex]\( x \)[/tex] on one side and the constants on the other side. Start by adding [tex]\( 14x \)[/tex] to both sides:

[tex]\[ -18 = 19x + 20 \][/tex]

Then, isolate [tex]\( x \)[/tex] by subtracting 20 from both sides:

[tex]\[ -18 - 20 = 19x \][/tex]

Simplify that equation:

[tex]\[ -38 = 19x \][/tex]

Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 19:

[tex]\[ x = \frac{-38}{19} \][/tex]

Simplify:

[tex]\[ x = -2 \][/tex]

Thus, the value of [tex]\( x \)[/tex] that makes the equation true is:

[tex]\[ \boxed{-2} \][/tex]

Therefore, the correct answer is:
A. -2
Wegnerkolmp2741oidn

Answer:

A. -2

Step-by-step explanation:

-12x - 2(x + 9) = 5(x + 4)

Distribute the 5 on the right hand side.

-12x - 2(x + 9) = 5x + 5(4)

-12x - 2(x + 9) = 5x + 20

Distribute the 2 on the left hand side.

-12x - 2x -18 = 5x + 20

Combine like terms.

-14x-18 = 5x+20

Add 14x to each side.

-14x-18 +14x= 5x+14x+20

-18 = 19x+20

Subtract 20 from each side.

-18-20 = 19x+20-20

-38 =19x

Divide each side by 19.

-38/1 19x/19

-2=x

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