In the equation below, m is a constant. \frac{3}{5}(5x - 10) - 2(x - m) = 18 If the soluti… — SAT

In the equation below, $m$ is a constant.

\frac{3}{5}(5x - 10) - 2(x - m) = 18

If the solution to the equation is $x = 12$ , what is the value of $m$ ?

Answer: 6

The correct value of

m

is 6.

Substituting

x = 12

into the equation yields

\frac{3}{5}(5(12) - 10) - 2(12 - m) = 18

, which simplifies to

30 - 24 + 2m = 18

. Combining constant terms gives

6 + 2m = 18

. Subtracting 6 from both sides gives

2m = 12

, and dividing by 2 yields

m = 6

Substitute

x = 12

into the given equation.

\frac{3}{5}(5(12) - 10) - 2(12 - m) = 18

Since

x = 12

is the solution, it must satisfy the equation.

Simplify the expression inside the first set of parentheses.

5(12) - 10 = 60 - 10 = 50

Evaluate the terms inside the parentheses first.

Multiply the simplified term by the fraction

\frac{3}{5}

\frac{3}{5}(50) = 30

Multiply 50 by 3 and divide by 5.

Substitute 30 back into the equation and distribute

-2

to the terms inside the second set of parentheses.

30 - 24 + 2m = 18

Distributing

-2

12 - m

yields

-24 + 2m

due to sign rules.

Combine the constant terms on the left side of the equation.

6 + 2m = 18

30 - 24 = 6

Subtract 6 from both sides to isolate the term with

m

2m = 12

Isolate the variable term on one side of the equation.

Divide both sides by 2 to solve for

m

m = 6

Divide 12 by 2 to find the final value.

Solving a linear equation in one variable by substitution and isolation.

Question