If x is a real number that satisfies the equation \frac{3}{5}(2x - 7) + 0.4 = 0.2(x + 3), … — ACT

If $x$ is a real number that satisfies the equation $\frac{3}{5}(2x - 7) + 0.4 = 0.2(x + 3)$ , what is the value of $5x - 2$ ?

Answer: 20

The value of the expression

5x - 2

20

First, convert the fraction

\frac{3}{5}

to the decimal

0.6

. The equation becomes

0.6(2x - 7) + 0.4 = 0.2(x + 3)

. Distribute on both sides to get

1.2x - 4.2 + 0.4 = 0.2x + 0.6

. Combine constant terms on the left side to get

1.2x - 3.8 = 0.2x + 0.6

. Subtract

0.2x

and add

3.8

to both sides to isolate the variable, resulting in

x = 4.4

. Finally, substitute

x = 4.4

into the expression

5x - 2

to get

5(4.4) - 2 = 22 - 2 = 20

Convert the fraction and distribute the coefficients

1.2x - 4.2 + 0.4 = 0.2x + 0.6

To clear parentheses and align terms using decimals.

Combine constants on the left side

1.2x - 3.8 = 0.2x + 0.6

To simplify the left-hand side of the linear equation.

Isolate the variable

x

x = 4.4

To determine the value of the unknown variable.

Evaluate the target expression

20

To compute the final value of the expression

5x - 2

Solving linear equations with fractional and decimal coefficients

Question