Question

Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the equation.

$\frac{2}{3}y+\frac{1}{2}\left(y-3\right)=\frac{y+1}{4}$

Short answer

The solution of the given equation is $y=\frac{21}{11}$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\frac{2}{3}y+\frac{1}{2}(y-3)=\frac{y+1}{4}$

Step 3. Solve the given equation.

LCM of $3,2,4$is $12$, so multiply both sides by$12$ to simplify the given equation.

role="math" localid="1643307748141" $$\begin{gathered} 12\left(\frac{2}{3}y+\frac{1}{2}(y-3)\right)=12\left(\frac{y+1}{4}\right) \\ 12\left(\frac{2}{3}y\right)+12\left(\frac{1}{2}(y-3)\right)=3\left(y+1\right) \\ 8y+6(y-3)=3\left(y+1\right) \\ 8y+6y-18=3y+3 \end{gathered}$$

Isolate variable terms.

role="math" localid="1643307784181" $\begin{array}{c}8y+6y-3y=3+18\\ 11y=21\end{array}$

Divide both sides by $11$.

$\begin{array}{c}\frac{11y}{11}=\frac{21}{11}\\ y=\frac{21}{11}\end{array}$

Thus, the solution of the given equation is $y=\frac{21}{11}$.