Flashcard 15 - Math Flashcard Set for the SAT Exam

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The correct answer is:

(blank) 1 / 6 or 1 / 6 (blank)


Explanation:

Distribute the 10 through the parentheses on the left-hand side of the equation to get:

\[\frac{10}{12} + 10x = \frac{5}{3} + 5x\]

Subtract 5x and \(\frac{10}{12}\) from both sides of the equation to obtain:

\[5x =\frac{5}{3} - \frac{10}{12}\]

Simplify.

\[5x = \frac{5}{3} - \frac{5}{6}\]

Eliminate the denominators by multiplying both sides of the equation by 6, the least common multiple of 3 and 6:

\[30x = \frac{30}{3} - \frac{30}{6} = 10 – 5 = 5\]

Isolate the variable on the left-hand side of 30x = 5 by dividing both sides of the equation by 30:

\[x = \frac{5}{30} = \frac{1}{6}\]

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