Answer :
To solve the equation [tex]\(10 + 6(-9 - 4x) = 10(x - 12) + 8\)[/tex], let's go through the steps methodically.
1. Expand and simplify both sides of the equation:
Start by distributing and simplifying each term:
[tex]\[ 10 + 6(-9 - 4x) = 10(x - 12) + 8 \][/tex]
For the left-hand side (LHS):
[tex]\[ 6(-9 - 4x) = 6(-9) + 6(-4x) = -54 - 24x \][/tex]
Thus,
[tex]\[ 10 + (-54 - 24x) = 10 - 54 - 24x = -44 - 24x \][/tex]
For the right-hand side (RHS):
[tex]\[ 10(x - 12) = 10x - 120 \][/tex]
Thus,
[tex]\[ 10x - 120 + 8 = 10x - 112 \][/tex]
Now the equation is:
[tex]\[ -44 - 24x = 10x - 112 \][/tex]
2. Combine like terms to solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], first add [tex]\(24x\)[/tex] to both sides of the equation:
[tex]\[ -44 - 24x + 24x = 10x - 112 + 24x \][/tex]
This simplifies to:
[tex]\[ -44 = 34x - 112 \][/tex]
Next, add 112 to both sides:
[tex]\[ -44 + 112 = 34x - 112 + 112 \][/tex]
This simplifies to:
[tex]\[ 68 = 34x \][/tex]
Finally, divide both sides by 34:
[tex]\[ \frac{68}{34} = x \][/tex]
Simplifies to:
[tex]\[ 2 = x \text{ or } x = 2 \][/tex]
3. Verification:
To confirm the solution, substitute [tex]\( x = 2 \)[/tex] back into the original equation:
LHS:
[tex]\[ 10 + 6(-9 - 4 \cdot 2) = 10 + 6(-9 - 8) = 10 + 6(-17) = 10 - 102 = -92 \][/tex]
RHS:
[tex]\[ 10(2 - 12) + 8 = 10(-10) + 8 = -100 + 8 = -92 \][/tex]
Since both sides equal [tex]\(-92\)[/tex], the solution [tex]\( x = 2 \)[/tex] is correct.
Therefore, the correct answer is:
[tex]\[ \boxed{x = 2} \][/tex]
So, the solution to the equation [tex]\(10 + 6(-9 - 4x) = 10(x - 12) + 8\)[/tex] is:
[tex]\[B. x = 2\][/tex]
1. Expand and simplify both sides of the equation:
Start by distributing and simplifying each term:
[tex]\[ 10 + 6(-9 - 4x) = 10(x - 12) + 8 \][/tex]
For the left-hand side (LHS):
[tex]\[ 6(-9 - 4x) = 6(-9) + 6(-4x) = -54 - 24x \][/tex]
Thus,
[tex]\[ 10 + (-54 - 24x) = 10 - 54 - 24x = -44 - 24x \][/tex]
For the right-hand side (RHS):
[tex]\[ 10(x - 12) = 10x - 120 \][/tex]
Thus,
[tex]\[ 10x - 120 + 8 = 10x - 112 \][/tex]
Now the equation is:
[tex]\[ -44 - 24x = 10x - 112 \][/tex]
2. Combine like terms to solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], first add [tex]\(24x\)[/tex] to both sides of the equation:
[tex]\[ -44 - 24x + 24x = 10x - 112 + 24x \][/tex]
This simplifies to:
[tex]\[ -44 = 34x - 112 \][/tex]
Next, add 112 to both sides:
[tex]\[ -44 + 112 = 34x - 112 + 112 \][/tex]
This simplifies to:
[tex]\[ 68 = 34x \][/tex]
Finally, divide both sides by 34:
[tex]\[ \frac{68}{34} = x \][/tex]
Simplifies to:
[tex]\[ 2 = x \text{ or } x = 2 \][/tex]
3. Verification:
To confirm the solution, substitute [tex]\( x = 2 \)[/tex] back into the original equation:
LHS:
[tex]\[ 10 + 6(-9 - 4 \cdot 2) = 10 + 6(-9 - 8) = 10 + 6(-17) = 10 - 102 = -92 \][/tex]
RHS:
[tex]\[ 10(2 - 12) + 8 = 10(-10) + 8 = -100 + 8 = -92 \][/tex]
Since both sides equal [tex]\(-92\)[/tex], the solution [tex]\( x = 2 \)[/tex] is correct.
Therefore, the correct answer is:
[tex]\[ \boxed{x = 2} \][/tex]
So, the solution to the equation [tex]\(10 + 6(-9 - 4x) = 10(x - 12) + 8\)[/tex] is:
[tex]\[B. x = 2\][/tex]
