Question $12+\frac{20}{x}=10$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes this equation true! Watch out! Remember, we can't divide by zero, so $x$ can't be zero.
Keep an eye out for that sneaky zero!

STEP 2

1. Isolate the fraction
2. Isolate $x$
3. Verify

STEP 3

We want to get the fraction with $x$ all by itself.
To do that, let's subtract 12 from both sides of the equation.
This keeps the equation balanced, like a seesaw! $12 + \frac{20}{x} - 12 = 10 - 12$ $\frac{20}{x} = -2$ Now we're getting closer!

STEP 4

To get $x$ out of the denominator, we multiply both sides by $x$ .
It's like untangling a knot! $\frac{20}{x} \cdot x = -2 \cdot x$ $20 = -2x$

STEP 5

Almost there!
Now, we divide both sides by -2 to get $x$ completely alone.
Dividing by -2 is the same as multiplying by $\frac{1}{-2}$ . $\frac{20}{-2} = \frac{-2x}{-2}$ $-10 = x$ So, we think $x = \mathbf{-10}$ !

STEP 6

Let's double-check our work by plugging our answer back into the original equation.
This is super important! $12 + \frac{20}{x} = 10$ $12 + \frac{20}{\mathbf{-10}} = 10$

STEP 7

$12 + (-2) = 10$

STEP 8

$10 = 10$ YES! Our equation is true, so our answer is correct!

STEP 9

$x = -10$

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