Solve 7(3x+1)+8(2x-3)=4(3x-1)-7(x-4)

$$7 ( 3 x + 1 ) + 8 ( 2 x - 3 ) = 4 ( 3 x - 1 ) - 7 ( x - 4 )$$

Solve for x

$$x = \frac{41}{32} = 1\frac{9}{32} = 1.28125$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 3x+1.

$$21x+7+8\left(2x-3\right)=4\left(3x-1\right)-7\left(x-4\right)$$

Use the distributive property to multiply 8 by 2x-3.

$$21x+7+16x-24=4\left(3x-1\right)-7\left(x-4\right)$$

Combine 21x and 16x to get 37x.

$$37x+7-24=4\left(3x-1\right)-7\left(x-4\right)$$

Subtract 24 from 7 to get -17.

$$37x-17=4\left(3x-1\right)-7\left(x-4\right)$$

Use the distributive property to multiply 4 by 3x-1.

$$37x-17=12x-4-7\left(x-4\right)$$

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

$$37x-17=12x-4-7x+28$$

Combine 12x and -7x to get 5x.

$$37x-17=5x-4+28$$

Add -4 and 28 to get 24.

$$37x-17=5x+24$$

Subtract 5x from both sides.

$$37x-17-5x=24$$

Combine 37x and -5x to get 32x.

$$32x-17=24$$

Add 17 to both sides.

$$32x=24+17$$

Add 24 and 17 to get 41.

$$32x=41$$

Divide both sides by 32.

$$x=\frac{41}{32}$$