From health tips to tech hacks, find it all on IDNLearn.com. Our experts provide timely, comprehensive responses to ensure you have the information you need.

Which equation is equivalent to the given equation?

-4(x-5) + 8x = 9x - 3

A. 5x = -12
B. -5x = -23
C. -5x = 2
D. 5x = 17


Sagot :

To determine which equation is equivalent to the given equation:

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

we should follow a series of algebraic steps. Let’s go through them methodically:

1. Distribute the [tex]\(-4\)[/tex] on the left side of the equation:
[tex]\[ -4(x-5) + 8x = 9x - 3 \][/tex]
[tex]\[ -4x + 20 + 8x = 9x - 3 \][/tex]

2. Combine like terms on the left side:
[tex]\[ (-4x + 8x) + 20 = 9x - 3 \][/tex]
[tex]\[ 4x + 20 = 9x - 3 \][/tex]

3. Isolate the [tex]\(x\)[/tex] terms on one side and the constants on the other. We'll move the [tex]\(9x\)[/tex] term from the right to the left:
[tex]\[ 4x - 9x + 20 = -3 \][/tex]
[tex]\[ -5x + 20 = -3 \][/tex]

4. Isolate the [tex]\(x\)[/tex] term by moving the constants to the other side:
[tex]\[ -5x = -3 - 20 \][/tex]
[tex]\[ -5x = -23 \][/tex]

Hence, the equation equivalent to the given equation is:
[tex]\[ -5x = -23 \][/tex]

This matches choice B. Therefore, the correct answer is:

[tex]\[ \boxed{B. \, -5x = -23} \][/tex]