Solve 0.7(2-5x)-0.5(3x-2)=3(3-4x)

$$0.7(2-5x)-0.5(3x-2)=3(3-4x)$$

Solve for x

$$x=\frac{33}{35}\approx 0.942857143$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.7 by 2-5x.

$$1.4-3.5x-0.5\left(3x-2\right)=3\left(3-4x\right)$$

Use the distributive property to multiply -0.5 by 3x-2.

$$1.4-3.5x-1.5x+1=3\left(3-4x\right)$$

Combine -3.5x and -1.5x to get -5x.

$$1.4-5x+1=3\left(3-4x\right)$$

Add 1.4 and 1 to get 2.4.

$$2.4-5x=3\left(3-4x\right)$$

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

$$2.4-5x=9-12x$$

Add 12x to both sides.

$$2.4-5x+12x=9$$

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

$$2.4+7x=9$$

Subtract 2.4 from both sides.

$$7x=9-2.4$$

Subtract 2.4 from 9 to get 6.6.

$$7x=6.6$$

Divide both sides by 7.

$$x=\frac{6.6}{7}$$

Expand \frac{6.6}{7} by multiplying both numerator and the denominator by 10.

$$x=\frac{66}{70}$$

Reduce the fraction \frac{66}{70} to lowest terms by extracting and canceling out 2.

$$x=\frac{33}{35}$$