Solve frac{3x_{1}+6}{8}=2x+10/6

$$\frac { 3 x _ { 1 } + 6 } { 8 } = \frac { 2 x + 10 } { 6 }$$

Solve for x

$$x=\frac{9x_{1}}{8}-\frac{11}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,6.

$$3\left(3x_{1}+6\right)=4\left(2x+10\right)$$

Use the distributive property to multiply 3 by 3x_{1}+6.

$$9x_{1}+18=4\left(2x+10\right)$$

Use the distributive property to multiply 4 by 2x+10.

$$9x_{1}+18=8x+40$$

Swap sides so that all variable terms are on the left hand side.

$$8x+40=9x_{1}+18$$

Subtract 40 from both sides.

$$8x=9x_{1}+18-40$$

Subtract 40 from 18 to get -22.

$$8x=9x_{1}-22$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{9x_{1}-22}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{9x_{1}-22}{8}$$

Divide 9x_{1}-22 by 8.

$$x=\frac{9x_{1}}{8}-\frac{11}{4}$$

Solve for x_1

$$x_{1}=\frac{8x+22}{9}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,6.

$$3\left(3x_{1}+6\right)=4\left(2x+10\right)$$

Use the distributive property to multiply 3 by 3x_{1}+6.

$$9x_{1}+18=4\left(2x+10\right)$$

Use the distributive property to multiply 4 by 2x+10.

$$9x_{1}+18=8x+40$$

Subtract 18 from both sides.

$$9x_{1}=8x+40-18$$

Subtract 18 from 40 to get 22.

$$9x_{1}=8x+22$$

Divide both sides by 9.

$$\frac{9x_{1}}{9}=\frac{8x+22}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x_{1}=\frac{8x+22}{9}$$