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Which equation is equivalent to the given equation?
[tex]\[ -4(x-5) + 8x = 9x - 3 \][/tex]

A. [tex]\( 5x = 17 \)[/tex]

B. [tex]\(-5x = -23\)[/tex]

C. [tex]\(5x = -12\)[/tex]

D. [tex]\(-5x = 2\)[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the given equation step-by-step to find an equivalent equation.

The given equation is:

[tex]\[ -4(x - 5) + 8x = 9x - 3 \][/tex]

1. First, distribute -4 to the terms inside the parentheses:

[tex]\[ -4 \cdot (x - 5) = -4x + 20 \][/tex]

So, the equation now becomes:

[tex]\[ -4x + 20 + 8x = 9x - 3 \][/tex]

2. Next, combine the like terms on the left-hand side:

[tex]\[ -4x + 8x = 4x \][/tex]

So, the equation simplifies to:

[tex]\[ 4x + 20 = 9x - 3 \][/tex]

3. Subtract 9x from both sides to move all terms involving [tex]\( x \)[/tex] to one side:

[tex]\[ 4x - 9x + 20 = -3 \][/tex]

This simplifies to:

[tex]\[ -5x + 20 = -3 \][/tex]

4. Subtract 20 from both sides to isolate the term involving [tex]\( x \)[/tex] on one side:

[tex]\[ -5x = -3 - 20 \][/tex]

Which simplifies to:

[tex]\[ -5x = -23 \][/tex]

So, the equation that is equivalent to the given equation is:

[tex]\[ -5x = -23 \][/tex]

Hence, the correct answer is:

B. [tex]\( -5x = -23 \)[/tex]
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