How to solve x-10=(5)/(9)(x-6)

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 x-10=(5)/(9)(x-6) | Equatix

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Question

$$x-10= \frac{ 5 }{ 9 } (x-6)$$

Solve for x

$x=15$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{5}{9}$ by $x-6$.

$$x-10=\frac{5}{9}x+\frac{5}{9}\left(-6\right)$$

Express $\frac{5}{9}\left(-6\right)$ as a single fraction.

$$x-10=\frac{5}{9}x+\frac{5\left(-6\right)}{9}$$

Multiply $5$ and $-6$ to get $-30$.

$$x-10=\frac{5}{9}x+\frac{-30}{9}$$

Reduce the fraction $\frac{-30}{9}$ to lowest terms by extracting and canceling out $3$.

$$x-10=\frac{5}{9}x-\frac{10}{3}$$

Subtract $\frac{5}{9}x$ from both sides.

$$x-10-\frac{5}{9}x=-\frac{10}{3}$$

Combine $x$ and $-\frac{5}{9}x$ to get $\frac{4}{9}x$.

$$\frac{4}{9}x-10=-\frac{10}{3}$$

Add $10$ to both sides.

$$\frac{4}{9}x=-\frac{10}{3}+10$$

Convert $10$ to fraction $\frac{30}{3}$.

$$\frac{4}{9}x=-\frac{10}{3}+\frac{30}{3}$$

Since $-\frac{10}{3}$ and $\frac{30}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{4}{9}x=\frac{-10+30}{3}$$

Add $-10$ and $30$ to get $20$.

$$\frac{4}{9}x=\frac{20}{3}$$

Multiply both sides by $\frac{9}{4}$, the reciprocal of $\frac{4}{9}$.

$$x=\frac{20}{3}\times \frac{9}{4}$$

Multiply $\frac{20}{3}$ times $\frac{9}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{20\times 9}{3\times 4}$$

Do the multiplications in the fraction $\frac{20\times 9}{3\times 4}$.

$$x=\frac{180}{12}$$

Divide $180$ by $12$ to get $15$.

$$x=15$$

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