Solve 7(x/2-5)=5(x/6-3)+20

$$7( \frac{ x }{ 2 } -5)=5( \frac{ x }{ 6 } -3)+20$$

Solve for x

$$x=15$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6.

$$42\left(\frac{x}{2}-5\right)=30\left(\frac{x}{6}-3\right)+120$$

Use the distributive property to multiply 42 by \frac{x}{2}-5.

$$42\times \frac{x}{2}-210=30\left(\frac{x}{6}-3\right)+120$$

Cancel out 2, the greatest common factor in 42 and 2.

$$21x-210=30\left(\frac{x}{6}-3\right)+120$$

Use the distributive property to multiply 30 by \frac{x}{6}-3.

$$21x-210=30\times \frac{x}{6}-90+120$$

Cancel out 6, the greatest common factor in 30 and 6.

$$21x-210=5x-90+120$$

Add -90 and 120 to get 30.

$$21x-210=5x+30$$

Subtract 5x from both sides.

$$21x-210-5x=30$$

Combine 21x and -5x to get 16x.

$$16x-210=30$$

Add 210 to both sides.

$$16x=30+210$$

Add 30 and 210 to get 240.

$$16x=240$$

Divide both sides by 16.

$$x=\frac{240}{16}$$

Divide 240 by 16 to get 15.

$$x=15$$