QuestionSolve for $x$ in the equation $x - \frac{5}{4} = \frac{2}{3}$ .

Studdy Solution

STEP 1

Question: What is the first step to isolate $x$ in the equation $x-\frac{5}{4}=\frac{2}{3}$ ?
A) Multiply $\frac{5}{4}$ by $x$ B) Add $\frac{5}{4}$ to both sides C) Subtract $\frac{2}{3}$ from both sides D) Divide $\frac{5}{4}$ by $x$
Answer: B) Add $\frac{5}{4}$ to both sides

STEP 2

Question: After adding $\frac{5}{4}$ to both sides, the equation becomes?
A) $x=\frac{2}{3}+\frac{5}{4}$ B) $x=\frac{7}{12}$ C) $x=\frac{2}{3}-\frac{5}{4}$ D) $x=\frac{7}{4}$
Answer: A) $x=\frac{2}{3}+\frac{5}{4}$

STEP 3

Question: What is the least common denominator (LCD) of $\frac{2}{3}$ and $\frac{5}{4}$ ?
A) 7 B) 12 C) 8 D) 4
Answer: B) 12

STEP 4

Question: Convert the fractions to have a common denominator of 12. What do you get?
A) $x=\frac{5}{12}+\frac{2}{12}$ B) $x=\frac{4}{12}+\frac{3}{12}$ C) $x=\frac{8}{12}+\frac{15}{12}$ D) $x=\frac{6}{12}+\frac{4}{12}$
Answer: C) $x=\frac{8}{12}+\frac{15}{12}$

STEP 5

Question: Simplify the equation from step 4. What is the solution for $x$ ?
A) $x=\frac{23}{12}$ B) $x=\frac{24}{12}$ C) $x=\frac{22}{12}$ D) $x=\frac{21}{12}$
Answer: A) $x=\frac{23}{12}$

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