Question

The value of $x$ that satisfies the equation $11(x+2)-5(x-2)=4(x+4)$ is _____.

• A. $-8$
• B. $8$
• C. $4$
• D. $-4$

Hint:

Always expand brackets carefully when negative signs are involved. For example: \[ -5(x-2)=-5x+10 \] Students often mistakenly write \(-5x-10\).

Answer 1

The Correct Option is A

Concept: To solve a linear equation:
• Remove brackets using distributive law
• Combine like terms
• Bring variable terms to one side
• Bring constants to the other side

Step 1: Expand the left-hand side.
Given equation: \[ 11(x+2)-5(x-2)=4(x+4) \] Distribute \(11\): \[ 11x+22 \] Distribute \(-5\): \[ -5x+10 \] Thus, \[ 11x+22-5x+10=4(x+4) \]

Step 2: Expand the right-hand side.
Distribute \(4\): \[ 4x+16 \] Therefore, \[ 11x+22-5x+10=4x+16 \]

Step 3: Combine like terms.
Combine variable terms on the left: \[ 11x-5x=6x \] Combine constants: \[ 22+10=32 \] So the equation becomes: \[ 6x+32=4x+16 \]

Step 4: Bring variable terms to one side.
Subtract \(4x\) from both sides: \[ 6x-4x+32=16 \] \[ 2x+32=16 \]

Step 5: Bring constants to the other side.
Subtract \(32\) from both sides: \[ 2x=16-32 \] \[ 2x=-16 \]

Step 6: Solve for \(x\).
Divide both sides by \(2\): \[ x=\frac{-16}{2} \] \[ x=-8 \] Therefore, \[ \boxed{x=-8} \]