Solve for q. 3(1/4q + 1) = q q = ____

Distribute Terms: Distribute 3 to each term inside the parentheses. 3 * (1/4q + 1) = 3 * 1/4q + 3 * 1 = 3/4q + 3 Isolate q: Rewrite the equation to isolate q on one side. 3/4q + 3 = q 3/4q + 3 - 3 = q - 3 (subtracting 3 from both sides) 3/4q = q - 3 Subtract q: Subtract q from both sides to isolate terms with q on one side. 3/4q - q = q - 3 - q 3/4q - q = -3 Combine Like Terms: Combine like terms. 3/4q - 4/4q = -3 -1/4q = -3 Solve for q: Solve for q by multiplying both sides by -4. -1/4q * -4 = -3 * -4 q = 12

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

q

\newline

3\left(\frac{1}{4}q + 1\right) = q

\newline

q = ____

Distribute Terms: Distribute $3$ to each term inside the parentheses. $\newline$ $3 \times (\frac{1}{4}q + 1) = 3 \times \frac{1}{4}q + 3 \times 1$ $\newline$ $= \frac{3}{4}q + 3$
Isolate q: Rewrite the equation to isolate q on one side. $\newline$ $\frac{3}{4}q + 3 = q$ $\newline$ $\frac{3}{4}q + 3 - 3 = q - 3$ (subtracting $3$ from both sides) $\newline$ $\frac{3}{4}q = q - 3$
Subtract $q$ : Subtract $q$ from both sides to isolate terms with $q$ on one side. $\newline$ $\frac{3}{4}q - q = q - 3 - q$ $\newline$ $\frac{3}{4}q - q = -3$
Combine Like Terms: Combine like terms. $\newline$ $\frac{3}{4}q - \frac{4}{4}q = -3$ $\newline$ $-\frac{1}{4}q = -3$
Solve for q: Solve for q by multiplying both sides by -4＂).$\newline\$-\frac{1}{4}q \times -4 = -3 \times -4$$\newline$$q = 12$