Solve 3(-x+4)+7(4x-14)=22x+1

$$3 ( - x + 4 ) + 7 ( 4 x - 14 ) = 22 x + 1$$

Solve for x

$$x=29$$

Steps for Solving Linear Equation

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

$$3\left(-x\right)+12+7\left(4x-14\right)=22x+1$$

Use the distributive property to multiply 7 by 4x-14.

$$3\left(-x\right)+12+28x-98=22x+1$$

Subtract 98 from 12 to get -86.

$$3\left(-x\right)-86+28x=22x+1$$

Subtract 22x from both sides.

$$3\left(-x\right)-86+28x-22x=1$$

Combine 28x and -22x to get 6x.

$$3\left(-x\right)-86+6x=1$$

Add 86 to both sides.

$$3\left(-x\right)+6x=1+86$$

Add 1 and 86 to get 87.

$$3\left(-x\right)+6x=87$$

Multiply 3 and -1 to get -3.

$$-3x+6x=87$$

Combine -3x and 6x to get 3x.

$$3x=87$$

Divide both sides by 3.

$$x=\frac{87}{3}$$

Divide 87 by 3 to get 29.

$$x=29$$