Tyler Lowe
01/24/2023 · Middle School
Solve and check. \[ 6[2-(2 x-4)]=2(6=3 x) \] \( x=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation
\[
6[2-(2x-4)]=2(6-3x),
\]
we will first simplify both sides step by step.
### Step 1: Simplify the left side
Start with the left side:
\[
6[2 - (2x - 4)].
\]
Distributing the negative sign inside the brackets:
\[
2 - (2x - 4) = 2 - 2x + 4 = 6 - 2x.
\]
Now, substitute this back into the left side:
\[
6[6 - 2x] = 36 - 12x.
\]
### Step 2: Simplify the right side
Now simplify the right side:
\[
2(6 - 3x) = 12 - 6x.
\]
### Step 3: Set the simplified sides equal
Now we have:
\[
36 - 12x = 12 - 6x.
\]
### Step 4: Solve for \( x \)
To isolate \( x \), first add \( 12x \) to both sides:
\[
36 = 12 - 6x + 12x,
\]
which simplifies to:
\[
36 = 12 + 6x.
\]
Next, subtract \( 12 \) from both sides:
\[
36 - 12 = 6x,
\]
which gives:
\[
24 = 6x.
\]
Now, divide both sides by \( 6 \):
\[
x = \frac{24}{6} = 4.
\]
### Step 5: Check the solution
Now we will check if \( x = 4 \) satisfies the original equation. Substitute \( x = 4 \) back into the original equation:
Left side:
\[
6[2 - (2(4) - 4)] = 6[2 - (8 - 4)] = 6[2 - 4] = 6[-2] = -12.
\]
Right side:
\[
2(6 - 3(4)) = 2(6 - 12) = 2[-6] = -12.
\]
Since both sides are equal:
\[
-12 = -12,
\]
the solution is verified.
Thus, the final answer is:
\[
x = 4.
\]
Quick Answer
The solution to the equation is \( x = 4 \).
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