Answer :
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]
[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]
