Solve 0.4(10x+16)=4.2(0.2x+5)

$$0.4 ( 10 x + 16 ) = 4.2 ( 0.2 x + 5 )$$

Solve for x

$$x = \frac{365}{79} = 4\frac{49}{79} \approx 4.620253165$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.4 by 10x+16.

$$4x+6.4=4.2\left(0.2x+5\right)$$

Use the distributive property to multiply 4.2 by 0.2x+5.

$$4x+6.4=0.84x+21$$

Subtract 0.84x from both sides.

$$4x+6.4-0.84x=21$$

Combine 4x and -0.84x to get 3.16x.

$$3.16x+6.4=21$$

Subtract 6.4 from both sides.

$$3.16x=21-6.4$$

Subtract 6.4 from 21 to get 14.6.

$$3.16x=14.6$$

Divide both sides by 3.16.

$$x=\frac{14.6}{3.16}$$

Expand \frac{14.6}{3.16} by multiplying both numerator and the denominator by 100.

$$x=\frac{1460}{316}$$

Reduce the fraction \frac{1460}{316} to lowest terms by extracting and canceling out 4.

$$x=\frac{365}{79}$$