Math  /  Algebra

Questionsolve for uu 3=7+2u-3=7+2 u implify your answer as much as possible. u=u=

Studdy Solution

STEP 1

What is this asking? We need to find the value of uu that makes the equation 3=7+2u-3 = 7 + 2u true. Watch out! Don't forget to keep track of the negative signs, they can be sneaky!

STEP 2

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

STEP 3

We want to get the 2u2u term by itself.
The equation says we have 7 *added* to 2u2u, so to get rid of the 7, we need to do the *opposite* operation.
The opposite of adding 7 is subtracting 7.
And remember, whatever we do to one side of the equation, we *must* do to the other side to keep things balanced!
37=7+2u7-3 - 7 = 7 + 2u - 7

STEP 4

On the left side, 37-3 - 7 gives us 10-10.
On the right side, 777 - 7 adds to zero, leaving us with just 2u2u.
So our equation now looks like this:
10=2u-10 = 2u

STEP 5

Now, we have 22 *multiplied* by uu.
To get uu all alone, we need to do the opposite of multiplication, which is division!
We'll divide *both* sides by **2**.
102=2u2\frac{-10}{2} = \frac{2u}{2}

STEP 6

On the left side, 10-10 divided by **2** gives us 5-5.
On the right side, 22 divided by **2** is **1**, and 1u1 \cdot u is just uu.
Awesome! We've solved for uu!
5=u-5 = u

STEP 7

u=5u = -5

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