Solve 4x+14(3-2x)+7=4-x+5(2-3x)

$$4 x + 14 ( 3 - 2 x ) + 7 = 4 - x + 5 ( 2 - 3 x )$$

Solve for x

$$x = \frac{35}{8} = 4\frac{3}{8} = 4.375$$

Steps for Solving Linear Equation

Use the distributive property to multiply 14 by 3-2x.

$$4x+42-28x+7=4-x+5\left(2-3x\right)$$

Combine 4x and -28x to get -24x.

$$-24x+42+7=4-x+5\left(2-3x\right)$$

Add 42 and 7 to get 49.

$$-24x+49=4-x+5\left(2-3x\right)$$

Use the distributive property to multiply 5 by 2-3x.

$$-24x+49=4-x+10-15x$$

Add 4 and 10 to get 14.

$$-24x+49=14-x-15x$$

Combine -x and -15x to get -16x.

$$-24x+49=14-16x$$

Add 16x to both sides.

$$-24x+49+16x=14$$

Combine -24x and 16x to get -8x.

$$-8x+49=14$$

Subtract 49 from both sides.

$$-8x=14-49$$

Subtract 49 from 14 to get -35.

$$-8x=-35$$

Divide both sides by -8.

$$x=\frac{-35}{-8}$$

Fraction \frac{-35}{-8} can be simplified to \frac{35}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{35}{8}$$