Solve frac{2x_{3}+1}{5}+5-x/4=1-38+2/6

$$\frac { 2 x _ { 3 } + 1 } { 5 } + \frac { 5 - x } { 4 } = 1 - \frac { 38 + 2 } { 6 }$$

Solve for x

$$x=\frac{8x_{3}}{5}+\frac{427}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,4,6.

$$12\left(2x_{3}+1\right)+15\left(5-x\right)=60-10\left(38+2\right)$$

Use the distributive property to multiply 12 by 2x_{3}+1.

$$24x_{3}+12+15\left(5-x\right)=60-10\left(38+2\right)$$

Use the distributive property to multiply 15 by 5-x.

$$24x_{3}+12+75-15x=60-10\left(38+2\right)$$

Add 12 and 75 to get 87.

$$24x_{3}+87-15x=60-10\left(38+2\right)$$

Add 38 and 2 to get 40.

$$24x_{3}+87-15x=60-10\times 40$$

Multiply -10 and 40 to get -400.

$$24x_{3}+87-15x=60-400$$

Subtract 400 from 60 to get -340.

$$24x_{3}+87-15x=-340$$

Subtract 24x_{3} from both sides.

$$87-15x=-340-24x_{3}$$

Subtract 87 from both sides.

$$-15x=-340-24x_{3}-87$$

Subtract 87 from -340 to get -427.

$$-15x=-427-24x_{3}$$

The equation is in standard form.

$$-15x=-24x_{3}-427$$

Divide both sides by -15.

$$\frac{-15x}{-15}=\frac{-24x_{3}-427}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x=\frac{-24x_{3}-427}{-15}$$

Divide -427-24x_{3} by -15.

$$x=\frac{8x_{3}}{5}+\frac{427}{15}$$

Solve for x_3

$$x_{3}=\frac{5x}{8}-\frac{427}{24}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,4,6.

$$12\left(2x_{3}+1\right)+15\left(5-x\right)=60-10\left(38+2\right)$$

Use the distributive property to multiply 12 by 2x_{3}+1.

$$24x_{3}+12+15\left(5-x\right)=60-10\left(38+2\right)$$

Use the distributive property to multiply 15 by 5-x.

$$24x_{3}+12+75-15x=60-10\left(38+2\right)$$

Add 12 and 75 to get 87.

$$24x_{3}+87-15x=60-10\left(38+2\right)$$

Add 38 and 2 to get 40.

$$24x_{3}+87-15x=60-10\times 40$$

Multiply -10 and 40 to get -400.

$$24x_{3}+87-15x=60-400$$

Subtract 400 from 60 to get -340.

$$24x_{3}+87-15x=-340$$

Subtract 87 from both sides.

$$24x_{3}-15x=-340-87$$

Subtract 87 from -340 to get -427.

$$24x_{3}-15x=-427$$

Add 15x to both sides.

$$24x_{3}=-427+15x$$

The equation is in standard form.

$$24x_{3}=15x-427$$

Divide both sides by 24.

$$\frac{24x_{3}}{24}=\frac{15x-427}{24}$$

Dividing by 24 undoes the multiplication by 24.

$$x_{3}=\frac{15x-427}{24}$$

Divide -427+15x by 24.

$$x_{3}=\frac{5x}{8}-\frac{427}{24}$$