Let's solve your equation step-by-step.
9
2
(8−x)+36=102−
5
2
(3x+24)
Step 1: Simplify both sides of the equation.
9
2
(8−x)+36=102−
5
2
(3x+24)
(
9
2
)(8)+(
9
2
)(−x)+36=102+
−15
2
x+−60(Distribute)
36+
−9
2
x+36=102+
−15
2
x+−60
(
−9
2
x)+(36+36)=(
−15
2
x)+(102+−60)(Combine Like Terms)
−9
2
x+72=
−15
2
x+42
−9
2
x+72=
−15
2
x+42
Step 2: Add 15/2x to both sides.
−9
2
x+72+
15
2
x=
−15
2
x+42+
15
2
x
3x+72=42
Step 3: Subtract 72 from both sides.
3x+72−72=42−72
3x=−30
Step 4: Divide both sides by 3.
3x
3
=
−30
3
x=−10
Answer:
x=−10