Question $7 x-(3 x+5)-8=\frac{1}{2}(8 x+20)-7 x+5$

Studdy Solution

STEP 1

What is this asking? We're asked to find the mystery value of $x$ that makes this crazy equation true! Watch out! Distributing correctly is key, especially with those negative signs lurking around.
Don't let them trick you!

STEP 2

1. Simplify each side
2. Isolate $x$
3. Solve for $x$

STEP 3

Let's tackle the left side first.
We've got $7x - (3x + 5) - 8$ .
We can distribute the negative sign across the parentheses, which is like multiplying by $-1$ .

STEP 4

So, $7x - (3x + 5) - 8$ becomes $7x - 3x - 5 - 8$ .
Combining like terms, we get $4x - 13$ .
Awesome!

STEP 5

Now, let's conquer the right side: $\frac{1}{2}(8x + 20) - 7x + 5$ .
Distribute the $\frac{1}{2}$ into the parentheses.
This is like dividing each term inside by $2$ .

STEP 6

So, we get $\frac{1}{2} \cdot 8x + \frac{1}{2} \cdot 20 - 7x + 5$ , which simplifies to $4x + 10 - 7x + 5$ .
Combining like terms gives us $-3x + 15$ .
Fantastic!

STEP 7

Now, our equation looks much simpler: $4x - 13 = -3x + 15$ .
Let's get all the $x$ terms on one side and the numbers on the other.

STEP 8

We can add $3x$ to both sides.
Remember, whatever we do to one side, we must do to the other to keep the equation balanced!
This gives us $4x - 13 + 3x = -3x + 15 + 3x$ , simplifying to $7x - 13 = 15$ .

STEP 9

Next, let's add $13$ to both sides to isolate the $x$ term: $7x - 13 + 13 = 15 + 13$ .
This simplifies to $7x = 28$ .
We're almost there!

STEP 10

Finally, we can divide both sides by $7$ to solve for $x$ : $\frac{7x}{7} = \frac{28}{7}$ .

STEP 11

This gives us our final answer: $x = 4$ !

STEP 12

$x = 4$

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