Answer :
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]
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]
