How to solve 2 - 43/y = 7 1/2

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.

Solve 2 - 43/y = 7 1/2 | Equatix

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Question

$$2-\frac{43}{y}=7\frac{1}{2}$$

Solve for y

$y = -\frac{86}{11} = -7\frac{9}{11} \approx -7.818181818$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2y$, the least common multiple of $y,2$.

$$2y\times 2-2\times 43=y\left(7\times 2+1\right)$$

Multiply $2$ and $2$ to get $4$.

$$4y-2\times 43=y\left(7\times 2+1\right)$$

Multiply $-2$ and $43$ to get $-86$.

$$4y-86=y\left(7\times 2+1\right)$$

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

$$4y-86=y\left(14+1\right)$$

Add $14$ and $1$ to get $15$.

$$4y-86=y\times 15$$

Subtract $y\times 15$ from both sides.

$$4y-86-y\times 15=0$$

Combine $4y$ and $-y\times 15$ to get $-11y$.

$$-11y-86=0$$

Add $86$ to both sides. Anything plus zero gives itself.

$$-11y=86$$

Divide both sides by $-11$.

$$y=\frac{86}{-11}$$

Fraction $\frac{86}{-11}$ can be rewritten as $-\frac{86}{11}$ by extracting the negative sign.

$$y=-\frac{86}{11}$$

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