Solve 51/2-31/4x=41/4x-17

$$5 \frac { 1 } { 2 } - 3 \frac { 1 } { 4 } x = 4 \frac { 1 } { 4 } x - 17$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

$$2\left(5\times 2+1\right)-\left(3\times 4+1\right)x=\left(4\times 4+1\right)x-68$$

Multiply 5 and 2 to get 10.

$$2\left(10+1\right)-\left(3\times 4+1\right)x=\left(4\times 4+1\right)x-68$$

Add 10 and 1 to get 11.

$$2\times 11-\left(3\times 4+1\right)x=\left(4\times 4+1\right)x-68$$

Multiply 2 and 11 to get 22.

$$22-\left(3\times 4+1\right)x=\left(4\times 4+1\right)x-68$$

Multiply 3 and 4 to get 12.

$$22-\left(12+1\right)x=\left(4\times 4+1\right)x-68$$

Add 12 and 1 to get 13.

$$22-13x=\left(4\times 4+1\right)x-68$$

Multiply 4 and 4 to get 16.

$$22-13x=\left(16+1\right)x-68$$

Add 16 and 1 to get 17.

$$22-13x=17x-68$$

Subtract 17x from both sides.

$$22-13x-17x=-68$$

Combine -13x and -17x to get -30x.

$$22-30x=-68$$

Subtract 22 from both sides.

$$-30x=-68-22$$

Subtract 22 from -68 to get -90.

$$-30x=-90$$

Divide both sides by -30.

$$x=\frac{-90}{-30}$$

Divide -90 by -30 to get 3.

$$x=3$$