Solve 1+7(15-3x)-(2x+48)=-34(5-x)+18(1-2x)

$$1+7(15-3x)-(2x+48)=-34(5-x)+18(1-2x)$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 15-3x.

$$1+105-21x-\left(2x+48\right)=-34\left(5-x\right)+18\left(1-2x\right)$$

Add 1 and 105 to get 106.

$$106-21x-\left(2x+48\right)=-34\left(5-x\right)+18\left(1-2x\right)$$

To find the opposite of 2x+48, find the opposite of each term.

$$106-21x-2x-48=-34\left(5-x\right)+18\left(1-2x\right)$$

Combine -21x and -2x to get -23x.

$$106-23x-48=-34\left(5-x\right)+18\left(1-2x\right)$$

Subtract 48 from 106 to get 58.

$$58-23x=-34\left(5-x\right)+18\left(1-2x\right)$$

Use the distributive property to multiply -34 by 5-x.

$$58-23x=-170+34x+18\left(1-2x\right)$$

Use the distributive property to multiply 18 by 1-2x.

$$58-23x=-170+34x+18-36x$$

Add -170 and 18 to get -152.

$$58-23x=-152+34x-36x$$

Combine 34x and -36x to get -2x.

$$58-23x=-152-2x$$

Add 2x to both sides.

$$58-23x+2x=-152$$

Combine -23x and 2x to get -21x.

$$58-21x=-152$$

Subtract 58 from both sides.

$$-21x=-152-58$$

Subtract 58 from -152 to get -210.

$$-21x=-210$$

Divide both sides by -21.

$$x=\frac{-210}{-21}$$

Divide -210 by -21 to get 10.

$$x=10$$