Math  /  Algebra

QuestionSolve equaltion for xx and Simpify 6x+57x=104x+76 x+5-7 x=10-4 x+7

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes the given equation true! Watch out! Be careful with the signs when combining like terms – it's easy to make a mistake there.

STEP 2

1. Combine Like Terms
2. Isolate the Variable
3. Find the Solution

STEP 3

We have 6x6x and 7x-7x on the left side of the equation.
Combining these gives us 6x7x=1x6x - 7x = -1x, or just x-x.
So, the left side becomes x+5-x + 5.
We did this to simplify the equation, making it easier to work with!

STEP 4

On the right side, we have 1010 and 77.
Adding those together gives us 10+7=1710 + 7 = 17.
The right side now looks like 174x17 - 4x.
Again, this simplifies things, bringing us closer to our solution!

STEP 5

Our equation now looks like this: x+5=174x-x + 5 = 17 - 4x We've made the equation much cleaner!

STEP 6

Let's add 4x4x to *both* sides of the equation.
This will move all the xx terms to the left side: x+5+4x=174x+4x-x + 5 + 4x = 17 - 4x + 4x 3x+5=173x + 5 = 17Remember, what we do to one side, we *must* do to the other to keep the equation balanced.

STEP 7

Now, subtract 55 from *both* sides to get the xx term by itself: 3x+55=1753x + 5 - 5 = 17 - 5 3x=123x = 12We're almost there!

STEP 8

To completely isolate xx, we divide *both* sides by 33: 3x3=123\frac{3x}{3} = \frac{12}{3} x=4x = 4Boom! We found the value of xx!

STEP 9

The solution to the equation 6x+57x=104x+76x + 5 - 7x = 10 - 4x + 7 is x=4x = 4.

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