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Math  /  Algebra

Question3x−4=8x=\begin{array}{r}3 x-4=8 \\ x=\end{array}

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes the equation 3x−4=83x - 4 = 8 true! Watch out! Don't forget to perform the same operation on *both* sides of the equation to keep it balanced.

STEP 2

1. Isolate the term with xx.
2. Solve for xx.

STEP 3

We want to get xx by itself.
The left side of the equation has 3x−43x - 4, and we want to get rid of that −4-4.
The opposite of subtracting 44 is *adding* 44, so let's **add** 4\bf{4} to *both* sides of the equation.
Remember, what we do to one side, we *must* do to the other to keep things balanced! 3x−4+4=8+43x - 4 + 4 = 8 + 4

STEP 4

Now, on the left side, −4+4-4 + 4 adds to zero, leaving us with just 3x3x.
On the right side, 8+4=128 + 4 = 12.
So our equation becomes: 3x=123x = 12 We're getting closer to finding our mystery xx!

STEP 5

We have 33 multiplied by xx, and we want to get xx all alone.
To do this, we need to divide both sides by 3\bf{3}.
Dividing 3x3x by 33 is like dividing 33 by 33 and multiplying by xx.
Since 33 divided by 33 is 11, we get 11 multiplied by xx, which is just xx.
Awesome! 3x3=123\frac{3x}{3} = \frac{12}{3}

STEP 6

On the left side, we have 3x3\frac{3x}{3}, which simplifies to xx.
On the right side, we have 123\frac{12}{3}, which equals 4\bf{4}.
Look at that!
We've solved for xx! x=4x = 4

STEP 7

We found that x=4x = \bf{4}!

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