For a certain value of x, the expression \frac{2}{5}x + 3 is equal to 11. What is the valu… — ACT

For a certain value of $x$ , the expression $\frac{2}{5}x + 3$ is equal to $11$ . What is the value of $2x + 5$ ?

To find the value of

2x + 5

, we first isolate the variable

x

in the equation

\frac{2}{5}x + 3 = 11

. Subtracting

3

from both sides gives

\frac{2}{5}x = 8

. Multiplying both sides by the reciprocal of the coefficient,

\frac{5}{2}

, yields

x = 8 \times \frac{5}{2} = 20

. Finally, substituting

x = 20

into the expression

2x + 5

gives

2(20) + 5 = 40 + 5 = 45

Set up the equation based on the text and subtract 3 from both sides of the equation to isolate the variable term.

\frac{2}{5}x = 8

To solve for

x

, we first need to isolate the term containing

x

Multiply both sides of the equation by

\frac{5}{2}

to solve for

x

x = 20

Multiplying by the reciprocal of the coefficient cancels the fraction, leaving

x

isolated.

Substitute

x = 20

into the expression

2x + 5

2(20) + 5 = 45

The question asks for the value of

2x + 5

, so we evaluate it using the solved value of

x

Solving Linear Equations

We can also multiply the entire equation by

5

first to eliminate the fraction:

2x + 15 = 55

. Subtracting

15

from both sides gives

2x = 40

. Since the target expression is

2x + 5

, we can simply add

5

to both sides of

2x = 40

to get

2x + 5 = 45

, avoiding the need to solve for

x

directly.

Estimated Time:45s

Question