Solve 5(3x-13)-3(5x+4)=33(x-4)

$$5 ( 3 x - 13 ) - 3 ( 5 x + 4 ) = 33 ( x - 4 )$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 3x-13.

$$15x-65-3\left(5x+4\right)=33\left(x-4\right)$$

Use the distributive property to multiply -3 by 5x+4.

$$15x-65-15x-12=33\left(x-4\right)$$

Combine 15x and -15x to get 0.

$$-65-12=33\left(x-4\right)$$

Subtract 12 from -65 to get -77.

$$-77=33\left(x-4\right)$$

Use the distributive property to multiply 33 by x-4.

$$-77=33x-132$$

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

$$33x-132=-77$$

Add 132 to both sides.

$$33x=-77+132$$

Add -77 and 132 to get 55.

$$33x=55$$

Divide both sides by 33.

$$x=\frac{55}{33}$$

Reduce the fraction \frac{55}{33} to lowest terms by extracting and canceling out 11.

$$x=\frac{5}{3}$$