Solve 3x+7/2-2x+4/3=3x+4/4+5

$$\frac { 3 x + 7 } { 2 } - \frac { 2 x + 4 } { 3 } = \frac { 3 x + 4 } { 4 } + 5$$

Solve for x

$$x=46$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6\left(3x+7\right)-4\left(2x+4\right)=3\left(3x+4\right)+60$$

Use the distributive property to multiply 6 by 3x+7.

$$18x+42-4\left(2x+4\right)=3\left(3x+4\right)+60$$

Use the distributive property to multiply -4 by 2x+4.

$$18x+42-8x-16=3\left(3x+4\right)+60$$

Combine 18x and -8x to get 10x.

$$10x+42-16=3\left(3x+4\right)+60$$

Subtract 16 from 42 to get 26.

$$10x+26=3\left(3x+4\right)+60$$

Use the distributive property to multiply 3 by 3x+4.

$$10x+26=9x+12+60$$

Add 12 and 60 to get 72.

$$10x+26=9x+72$$

Subtract 9x from both sides.

$$10x+26-9x=72$$

Combine 10x and -9x to get x.

$$x+26=72$$

Subtract 26 from both sides.

$$x=72-26$$

Subtract 26 from 72 to get 46.

$$x=46$$