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Math  /  Algebra

Question3x=−2x=\begin{array}{r}3 x=-2 \\ x=\end{array}

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes the equation 3x=−23x = -2 true. Watch out! Don't forget that dividing by a number is the same as multiplying by its reciprocal.
Also, be careful with the negative sign!

STEP 2

1. Isolate xx
2. Celebrate!

STEP 3

We have the equation 3x=−23x = -2.
Our goal is to get xx all by itself.
Right now, xx is being multiplied by **3**.

STEP 4

To get xx alone, we need to undo the multiplication by **3**.
We can do this by dividing both sides of the equation by **3**.
Remember, what we do to one side, we *must* do to the other to keep the equation balanced!
Think of it like a seesaw – if you add weight to one side, you need to add the same weight to the other side to keep it level.

STEP 5

Dividing both sides by **3** gives us: 3x3=−23 \frac{3x}{3} = \frac{-2}{3} On the left side, the **3**'s divide to one, leaving us with just xx: 33⋅x=−23 \frac{3}{3} \cdot x = \frac{-2}{3} 1⋅x=−23 1 \cdot x = \frac{-2}{3} x=−23 x = \frac{-2}{3} So, we have x=−23x = \frac{-2}{3}.
Awesome!

STEP 6

Our **final answer** is x=−23x = \frac{-2}{3}.

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