Solve (x + 4)/(x - 4) = - 4/5 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x+4}{x-4}=\frac{-4}{5}$$

Solve for x

$x=-\frac{4}{9}\approx -0.444444444$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $4$ since division by zero is not defined. Multiply both sides of the equation by $5\left(x-4\right)$, the least common multiple of $x-4,5$.

$$5\left(x+4\right)=\left(x-4\right)\left(-4\right)$$

Use the distributive property to multiply $5$ by $x+4$.

$$5x+20=\left(x-4\right)\left(-4\right)$$

Use the distributive property to multiply $x-4$ by $-4$.

$$5x+20=-4x+16$$

Add $4x$ to both sides.

$$5x+20+4x=16$$

Combine $5x$ and $4x$ to get $9x$.

$$9x+20=16$$

Subtract $20$ from both sides.

$$9x=16-20$$

Subtract $20$ from $16$ to get $-4$.

$$9x=-4$$

Divide both sides by $9$.

$$x=\frac{-4}{9}$$

Fraction $\frac{-4}{9}$ can be rewritten as $-\frac{4}{9}$ by extracting the negative sign.

$$x=-\frac{4}{9}$$