Solve -10+(\ )=3 ( a)-10 | Equatix

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Question

$$- 10 + ( \frac { 1 } { ( a ) - 10 } ) = 3$$

Solve for a

$a = \frac{131}{13} = 10\frac{1}{13} \approx 10.076923077$

Steps for Solving Linear Equation

Variable $a$ cannot be equal to $10$ since division by zero is not defined. Multiply both sides of the equation by $a-10$.

$$\left(a-10\right)\left(-10\right)+1=3\left(a-10\right)$$

Use the distributive property to multiply $a-10$ by $-10$.

$$-10a+100+1=3\left(a-10\right)$$

Add $100$ and $1$ to get $101$.

$$-10a+101=3\left(a-10\right)$$

Use the distributive property to multiply $3$ by $a-10$.

$$-10a+101=3a-30$$

Subtract $3a$ from both sides.

$$-10a+101-3a=-30$$

Combine $-10a$ and $-3a$ to get $-13a$.

$$-13a+101=-30$$

Subtract $101$ from both sides.

$$-13a=-30-101$$

Subtract $101$ from $-30$ to get $-131$.

$$-13a=-131$$

Divide both sides by $-13$.

$$a=\frac{-131}{-13}$$

Fraction $\frac{-131}{-13}$ can be simplified to $\frac{131}{13}$ by removing the negative sign from both the numerator and the denominator.

$$a=\frac{131}{13}$$

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