If \frac{3}{5}x - 7 = 8, what is the value of 2x - 3? — ACT

If $\frac{3}{5}x - 7 = 8$ , what is the value of $2x - 3$ ?

To find the value of

2x - 3

, first solve the equation

\frac{3}{5}x - 7 = 8

for

x

. Adding 7 to both sides of the equation gives

\frac{3}{5}x = 15

. Multiplying both sides by the reciprocal

\frac{5}{3}

yields

x = 25

. Finally, substitute

25

for

x

in the expression

2x - 3

to get

2(25) - 3 = 50 - 3 = 47

Add 7 to both sides of the equation

\frac{3}{5}x - 7 = 8

to isolate the variable term.

\frac{3}{5}x = 15

Adding 7 to both sides eliminates the constant on the left side of the equation.

Multiply both sides of the equation by

\frac{5}{3}

to solve for

x

x = 25

Multiplying by the reciprocal of

\frac{3}{5}

isolates

x

on the left side of the equation.

Substitute

x = 25

into the expression

2x - 3

2(25) - 3 = 50 - 3 = 47

The question asks for the value of the expression

2x - 3

rather than just the variable

x

Solving two-step linear equations involving fractions, and evaluating algebraic expressions.

Instead of solving for

x

first, you can express the target expression in terms of

\frac{3}{5}x

. Specifically, note that

2x - 3 = \frac{10}{3}(\frac{3}{5}x) - 3

. Since

\frac{3}{5}x = 15

, substituting this directly gives

\frac{10}{3}(15) - 3 = 50 - 3 = 47

Estimated Time:45s

Question