How to solve 2y+11/4=1/3y+2

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$2y+11/4=1/3y+2$$

Solve for y

$y=-\frac{9}{20}=-0.45$

Steps for Solving Linear Equation

Subtract $\frac{1}{3}y$ from both sides.

$$2y+\frac{11}{4}-\frac{1}{3}y=2$$

Combine $2y$ and $-\frac{1}{3}y$ to get $\frac{5}{3}y$.

$$\frac{5}{3}y+\frac{11}{4}=2$$

Subtract $\frac{11}{4}$ from both sides.

$$\frac{5}{3}y=2-\frac{11}{4}$$

Convert $2$ to fraction $\frac{8}{4}$.

$$\frac{5}{3}y=\frac{8}{4}-\frac{11}{4}$$

Since $\frac{8}{4}$ and $\frac{11}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}y=\frac{8-11}{4}$$

Subtract $11$ from $8$ to get $-3$.

$$\frac{5}{3}y=-\frac{3}{4}$$

Multiply both sides by $\frac{3}{5}$, the reciprocal of $\frac{5}{3}$.

$$y=-\frac{3}{4}\times \frac{3}{5}$$

Multiply $-\frac{3}{4}$ times $\frac{3}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-3\times 3}{4\times 5}$$

Do the multiplications in the fraction $\frac{-3\times 3}{4\times 5}$.

$$y=\frac{-9}{20}$$

Fraction $\frac{-9}{20}$ can be rewritten as $-\frac{9}{20}$ by extracting the negative sign.

$$y=-\frac{9}{20}$$

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