Math  /  Algebra

QuestionSolve the equation. 6x3(x+8)=9x=\begin{array}{l} 6 x-3(x+8)=9 \\ x=\square \end{array}

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes the equation 6x3(x+8)=96x - 3(x + 8) = 9 true. Watch out! Don't forget to distribute the 3-3 to *both* xx and 88 inside the parentheses!

STEP 2

1. Distribute and Simplify
2. Isolate the Variable
3. Find the Solution

STEP 3

Alright, let's **kick things off** by distributing the 3-3 to both terms inside the parentheses.
Remember, this means multiplying 3-3 by both xx and 88.
So, we get: 6x+(3)x+(3)8=96x + (-3) \cdot x + (-3) \cdot 8 = 9 6x3x24=96x - 3x - 24 = 9

STEP 4

Now, let's **tidy things up** a bit by combining the xx terms.
We have 6x6x and 3x-3x, which combine to give us 3x3x.
Our equation now looks like this: 3x24=93x - 24 = 9

STEP 5

To **get** x\boldsymbol{x} **by itself**, we need to move that 24-24 to the other side of the equation.
We can do this by adding 2424 to both sides: 3x24+24=9+243x - 24 + 24 = 9 + 24 3x=333x = 33

STEP 6

Almost there!
Now, we just need to **isolate** x\boldsymbol{x} completely.
Since xx is being multiplied by 33, we'll divide both sides of the equation by 33: 3x3=333\frac{3x}{3} = \frac{33}{3} x=11x = 11

STEP 7

Boom! We found it!
Our **final answer** is x=11x = 11.

STEP 8

x=11x = 11

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