Solve for r. Give an exact answer. (1)/(2)r-3=3(4-(3)/(2)r) r=

Distribute and Simplify: Simplify the equation by distributing the 3 on the right side. (1)/(2)r - 3 = 3(4 - (3)/(2)r) = (1)/(2)r - 3 = 12 - (9)/(2)rRearrange Terms: Move all terms involving r to one side of the equation and constant terms to the other side. (1)/(2)r + (9)/(2)r = 12 + 3Combine Like Terms: Combine like terms. (1)/(2)r + (9)/(2)r = (10)/(2)r 10/2r = 15Simplify Fraction: Simplify the fraction on the left side. 5r = 15Divide to Solve: Divide both sides by 5 to solve for r. 5r / 5 = 15 / 5 r = 3

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Math Problems

Algebra 1

Solve multi-step linear equations

Full solution

Q. Solve for

r

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Give an exact answer.

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\frac{1}{2} r-3=3\left(4-\frac{3}{2} r\right)

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r = $\square$

Distribute and Simplify: Simplify the equation by distributing the $3$ on the right side. $\newline$ $\frac{1}{2}r - 3 = 3(4 - \frac{3}{2}r)$ $\newline$ $= \frac{1}{2}r - 3 = 12 - \frac{9}{2}r$
Rearrange Terms: Move all terms involving $r$ to one side of the equation and constant terms to the other side. $\frac{1}{2}r + \frac{9}{2}r = 12 + 3$
Combine Like Terms: Combine like terms. $\newline$ rac{1}{2}r + rac{9}{2}r = rac{10}{2}r $\newline$ $10/2r = 15$
Simplify Fraction: Simplify the fraction on the left side. $\newline$ $5r = 15$
Divide to Solve: Divide both sides by $5$ to solve for $r$ . $\frac{5r}{5} = \frac{15}{5}$ $r = 3$