# Solve for x (x+2)/(2x+5)=2/3

x+22x+5=23
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
(x+2)⋅3=(2x+5)⋅2
Solve the equation for x.
Simplify (x+2)⋅3.
Apply the distributive property.
x⋅3+2⋅3=(2x+5)⋅2
Simplify the expression.
Move 3 to the left of x.
3⋅x+2⋅3=(2x+5)⋅2
Multiply 2 by 3.
3x+6=(2x+5)⋅2
3x+6=(2x+5)⋅2
3x+6=(2x+5)⋅2
Simplify (2x+5)⋅2.
Apply the distributive property.
3x+6=2x⋅2+5⋅2
Multiply.
Multiply 2 by 2.
3x+6=4x+5⋅2
Multiply 5 by 2.
3x+6=4x+10
3x+6=4x+10
3x+6=4x+10
Move all terms containing x to the left side of the equation.
Subtract 4x from both sides of the equation.
3x+6-4x=10
Subtract 4x from 3x.
-x+6=10
-x+6=10
Move all terms not containing x to the right side of the equation.
Subtract 6 from both sides of the equation.
-x=10-6
Subtract 6 from 10.
-x=4
-x=4
Multiply each term in -x=4 by -1
Multiply each term in -x=4 by -1.
(-x)⋅-1=4⋅-1
Multiply (-x)⋅-1.
Multiply -1 by -1.
1x=4⋅-1
Multiply x by 1.
x=4⋅-1
x=4⋅-1
Multiply 4 by -1.
x=-4
x=-4
x=-4
Solve for x (x+2)/(2x+5)=2/3