Solve 5(2x-3)-3(2x-1)-48=4(x+3)-4(4x+7)+30

$$5(2x-3)-3(2x-1)-48=4(x+3)-4(4x+7)+30$$

Solve for x

$$x = \frac{37}{8} = 4\frac{5}{8} = 4.625$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2x-3.

$$10x-15-3\left(2x-1\right)-48=4\left(x+3\right)-4\left(4x+7\right)+30$$

Use the distributive property to multiply -3 by 2x-1.

$$10x-15-6x+3-48=4\left(x+3\right)-4\left(4x+7\right)+30$$

Combine 10x and -6x to get 4x.

$$4x-15+3-48=4\left(x+3\right)-4\left(4x+7\right)+30$$

Add -15 and 3 to get -12.

$$4x-12-48=4\left(x+3\right)-4\left(4x+7\right)+30$$

Subtract 48 from -12 to get -60.

$$4x-60=4\left(x+3\right)-4\left(4x+7\right)+30$$

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

$$4x-60=4x+12-4\left(4x+7\right)+30$$

Use the distributive property to multiply -4 by 4x+7.

$$4x-60=4x+12-16x-28+30$$

Combine 4x and -16x to get -12x.

$$4x-60=-12x+12-28+30$$

Subtract 28 from 12 to get -16.

$$4x-60=-12x-16+30$$

Add -16 and 30 to get 14.

$$4x-60=-12x+14$$

Add 12x to both sides.

$$4x-60+12x=14$$

Combine 4x and 12x to get 16x.

$$16x-60=14$$

Add 60 to both sides.

$$16x=14+60$$

Add 14 and 60 to get 74.

$$16x=74$$

Divide both sides by 16.

$$x=\frac{74}{16}$$

Reduce the fraction \frac{74}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{37}{8}$$