If \frac{2}{5}(3x - 4) - \frac{1}{3}(2x + 5) = \frac{1}{5}x + \frac{11}{15}, what is the v… — SAT

If $\frac{2}{5}(3x - 4) - \frac{1}{3}(2x + 5) = \frac{1}{5}x + \frac{11}{15}$ , what is the value of $2x - 7$ ?

Answer: 17

The correct answer is 17.

To find the value of

2x - 7

, first solve the linear equation for

x

. Distributing the coefficients on the left side of the equation gives

\frac{6}{5}x - \frac{8}{5} - \frac{2}{3}x - \frac{5}{3} = \frac{1}{5}x + \frac{11}{15}

. Combining the variable terms and constants on the left side results in

\frac{8}{15}x - \frac{49}{15} = \frac{3}{15}x + \frac{11}{15}

. Subtracting

\frac{3}{15}x

and adding

\frac{49}{15}

to both sides yields

\frac{5}{15}x = \frac{60}{15}

, which simplifies to

\frac{1}{3}x = 4

, or

x = 12

. Finally, substituting 12 into the expression

2x - 7

gives

2(12) - 7 = 17

Distribute the coefficients to the terms inside the parentheses.

\frac{6}{5}x - \frac{8}{5} - \frac{2}{3}x - \frac{5}{3} = \frac{1}{5}x + \frac{11}{15}

To eliminate parentheses and allow grouping of like terms.

Combine the variable terms and the constant terms on the left side using a common denominator of 15.

\frac{8}{15}x - \frac{49}{15} = \frac{3}{15}x + \frac{11}{15}

To simplify the linear equation into a standard two-sided form.

Subtract the variable term from the right side and add the constant term from the left side.

\frac{5}{15}x = \frac{60}{15}

, which simplifies to

x = 12

To isolate the variable

x

on one side of the equation.

Evaluate the expression

2x - 7

using the value of

x

2(12) - 7 = 17

To solve for the final requested quantity.

Linear Equations in One Variable

Question