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What is the value of \( x \) in the equation \( 6(x+1) - 5x = 8 + 2(x-1) \)?

A. \( 0 \)
B. \( \frac{5}{4} \)
C. \( \frac{7}{4} \)
D. [tex]\( 12 \)[/tex]

Sagot :

GinnyAnswer
To find the value of \( x \) in the given equation \( 6(x+1)-5x=8+2(x-1) \), follow these steps:

1. Expand both sides of the equation:

On the left side:
[tex]\[ 6(x + 1) - 5x \][/tex]
Distribute the \( 6 \):
[tex]\[ 6x + 6 - 5x \][/tex]
Combine like terms:
[tex]\[ x + 6 \][/tex]

On the right side:
[tex]\[ 8 + 2(x - 1) \][/tex]
Distribute the \( 2 \):
[tex]\[ 8 + 2x - 2 \][/tex]
Combine like terms:
[tex]\[ 2x + 6 \][/tex]

2. Set the simplified expressions from both sides equal to each other:
[tex]\[ x + 6 = 2x + 6 \][/tex]

3. Solve for \( x \):

Subtract \( x \) from both sides to isolate the variable term on one side:
[tex]\[ 6 = 2x + 6 - x \][/tex]
Simplify:
[tex]\[ 6 = x + 6 \][/tex]

Subtract \( 6 \) from both sides:
[tex]\[ 6 - 6 = x + 6 - 6 \][/tex]
Simplify:
[tex]\[ 0 = x \][/tex]

Therefore, the value of \( x \) is \( 0 \).

The correct answer is:
[tex]\[ 0 \][/tex]
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