# Solve for x (x-18)/8=(x-9)/12+5/24

x-188=x-912+524
Multiply both sides of the equation by 8.
x-18=(x-912+524)⋅(8)
Remove parentheses.
x-18=(x-912+524)⋅(8)
Simplify (x-912+524)⋅(8).
To write x-912 as a fraction with a common denominator, multiply by 22.
x-18=(x-912⋅22+524)⋅8
Write each expression with a common denominator of 24, by multiplying each by an appropriate factor of 1.
Multiply x-912 and 22.
x-18=((x-9)⋅212⋅2+524)⋅8
Multiply 12 by 2.
x-18=((x-9)⋅224+524)⋅8
x-18=((x-9)⋅224+524)⋅8
Combine the numerators over the common denominator.
x-18=(x-9)⋅2+524⋅8
Simplify the numerator.
Apply the distributive property.
x-18=x⋅2-9⋅2+524⋅8
Move 2 to the left of x.
x-18=2⋅x-9⋅2+524⋅8
Multiply -9 by 2.
x-18=2⋅x-18+524⋅8
x-18=2x-1324⋅8
x-18=2x-1324⋅8
Cancel the common factor of 8.
Factor 8 out of 24.
x-18=2x-138(3)⋅8
Cancel the common factor.
x-18=2x-138⋅3⋅8
Rewrite the expression.
x-18=2x-133
x-18=2x-133
x-18=2x-133
Move all terms containing x to the left side of the equation.
Subtract 2x-133 from both sides of the equation.
x-18-2x-133=0
To write x as a fraction with a common denominator, multiply by 33.
x⋅33-2x-133-18=0
Combine x and 33.
x⋅33-2x-133-18=0
Combine the numerators over the common denominator.
x⋅3-(2x-13)3-18=0
Simplify the numerator.
Move 3 to the left of x.
3⋅x-(2x-13)3-18=0
Apply the distributive property.
3x-(2x)–133-18=0
Multiply 2 by -1.
3x-2x–133-18=0
Multiply -1 by -13.
3x-2x+133-18=0
Subtract 2x from 3x.
x+133-18=0
x+133-18=0
To write -18 as a fraction with a common denominator, multiply by 33.
x+133-18⋅33=0
Combine -18 and 33.
x+133+-18⋅33=0
Combine the numerators over the common denominator.
x+13-18⋅33=0
Simplify the numerator.
Multiply -18 by 3.
x+13-543=0
Subtract 54 from 13.
x-413=0
x-413=0
x-413=0
Multiply both sides of the equation by 3.
3⋅x-413=3⋅0
Simplify both sides of the equation.
Cancel the common factor of 3.
Cancel the common factor.
3⋅x-413=3⋅0
Rewrite the expression.
x-41=3⋅0
x-41=3⋅0
Multiply 3 by 0.
x-41=0
x-41=0
Add 41 to both sides of the equation.
x=41
Solve for x (x-18)/8=(x-9)/12+5/24