How to solve 4y=(2)/(3)(3y-7)

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.

Solve 4y=(2)/(3)(3y-7) | Equatix

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Question

$$4y= \frac{ 2 }{ 3 } (3y-7)$$

Solve for y

$y = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{2}{3}$ by $3y-7$.

$$4y=\frac{2}{3}\times 3y+\frac{2}{3}\left(-7\right)$$

Cancel out $3$ and $3$.

$$4y=2y+\frac{2}{3}\left(-7\right)$$

Express $\frac{2}{3}\left(-7\right)$ as a single fraction.

$$4y=2y+\frac{2\left(-7\right)}{3}$$

Multiply $2$ and $-7$ to get $-14$.

$$4y=2y+\frac{-14}{3}$$

Fraction $\frac{-14}{3}$ can be rewritten as $-\frac{14}{3}$ by extracting the negative sign.

$$4y=2y-\frac{14}{3}$$

Subtract $2y$ from both sides.

$$4y-2y=-\frac{14}{3}$$

Combine $4y$ and $-2y$ to get $2y$.

$$2y=-\frac{14}{3}$$

Divide both sides by $2$.

$$y=\frac{-\frac{14}{3}}{2}$$

Express $\frac{-\frac{14}{3}}{2}$ as a single fraction.

$$y=\frac{-14}{3\times 2}$$

Multiply $3$ and $2$ to get $6$.

$$y=\frac{-14}{6}$$

Reduce the fraction $\frac{-14}{6}$ to lowest terms by extracting and canceling out $2$.

$$y=-\frac{7}{3}$$

Show Solution