Solve 4(x-8)+7(14-x)=5(x+9)-2(x+10)-1

$$4 ( x - 8 ) + 7 ( 14 - x ) = 5 ( x + 9 ) - 2 ( x + 10 ) - 1$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-8.

$$4x-32+7\left(14-x\right)=5\left(x+9\right)-2\left(x+10\right)-1$$

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

$$4x-32+98-7x=5\left(x+9\right)-2\left(x+10\right)-1$$

Add -32 and 98 to get 66.

$$4x+66-7x=5\left(x+9\right)-2\left(x+10\right)-1$$

Combine 4x and -7x to get -3x.

$$-3x+66=5\left(x+9\right)-2\left(x+10\right)-1$$

Use the distributive property to multiply 5 by x+9.

$$-3x+66=5x+45-2\left(x+10\right)-1$$

Use the distributive property to multiply -2 by x+10.

$$-3x+66=5x+45-2x-20-1$$

Combine 5x and -2x to get 3x.

$$-3x+66=3x+45-20-1$$

Subtract 20 from 45 to get 25.

$$-3x+66=3x+25-1$$

Subtract 1 from 25 to get 24.

$$-3x+66=3x+24$$

Subtract 3x from both sides.

$$-3x+66-3x=24$$

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

$$-6x+66=24$$

Subtract 66 from both sides.

$$-6x=24-66$$

Subtract 66 from 24 to get -42.

$$-6x=-42$$

Divide both sides by -6.

$$x=\frac{-42}{-6}$$

Divide -42 by -6 to get 7.

$$x=7$$