Solve 3(4x-3)-(x+7)=5(10-x)+2

$$3 ( 4 x - 3 ) - ( x + 7 ) = 5 ( 10 - x ) + 2$$

Solve for x

$$x = \frac{17}{4} = 4\frac{1}{4} = 4.25$$

Steps for Solving Linear Equation

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

$$12x-9-\left(x+7\right)=5\left(10-x\right)+2$$

To find the opposite of x+7, find the opposite of each term.

$$12x-9-x-7=5\left(10-x\right)+2$$

Combine 12x and -x to get 11x.

$$11x-9-7=5\left(10-x\right)+2$$

Subtract 7 from -9 to get -16.

$$11x-16=5\left(10-x\right)+2$$

Use the distributive property to multiply 5 by 10-x.

$$11x-16=50-5x+2$$

Add 50 and 2 to get 52.

$$11x-16=52-5x$$

Add 5x to both sides.

$$11x-16+5x=52$$

Combine 11x and 5x to get 16x.

$$16x-16=52$$

Add 16 to both sides.

$$16x=52+16$$

Add 52 and 16 to get 68.

$$16x=68$$

Divide both sides by 16.

$$x=\frac{68}{16}$$

Reduce the fraction \frac{68}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{17}{4}$$