Solve 4(7x-9)-10(3x+4)=40(1-x)

$$4(7x-9)-10(3x+4)=40(1-x)$$

Solve for x

$$x = \frac{58}{19} = 3\frac{1}{19} \approx 3.052631579$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 7x-9.

$$28x-36-10\left(3x+4\right)=40\left(1-x\right)$$

Use the distributive property to multiply -10 by 3x+4.

$$28x-36-30x-40=40\left(1-x\right)$$

Combine 28x and -30x to get -2x.

$$-2x-36-40=40\left(1-x\right)$$

Subtract 40 from -36 to get -76.

$$-2x-76=40\left(1-x\right)$$

Use the distributive property to multiply 40 by 1-x.

$$-2x-76=40-40x$$

Add 40x to both sides.

$$-2x-76+40x=40$$

Combine -2x and 40x to get 38x.

$$38x-76=40$$

Add 76 to both sides.

$$38x=40+76$$

Add 40 and 76 to get 116.

$$38x=116$$

Divide both sides by 38.

$$x=\frac{116}{38}$$

Reduce the fraction \frac{116}{38} to lowest terms by extracting and canceling out 2.

$$x=\frac{58}{19}$$