Asked by meoww :3
What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14?
Group of answer choices
-8
-1
1
8
Group of answer choices
-8
-1
1
8
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \(3x + 2(x - 9) = 8x + x - 14\), we will first simplify each side of the equation step by step.
Starting with the left side:
1. Distribute \(2\) in the term \(2(x - 9)\):
\[
3x + 2x - 18
\]
Combining like terms:
\[
5x - 18
\]
Now the left side becomes:
\[
5x - 18
\]
Now for the right side:
1. Combine like terms:
\[
8x + x - 14 = 9x - 14
\]
Now we have the simplified equation:
\[
5x - 18 = 9x - 14
\]
Next, we'll isolate \(x\) by getting all terms involving \(x\) on one side and the constant terms on the other:
1. Subtract \(5x\) from both sides:
\[
-18 = 9x - 5x - 14
\]
This simplifies to:
\[
-18 = 4x - 14
\]
2. Add \(14\) to both sides:
\[
-18 + 14 = 4x
\]
This simplifies to:
\[
-4 = 4x
\]
3. Divide both sides by \(4\):
\[
x = -1
\]
Thus, the solution to the equation is:
\[
\boxed{-1}
\]
Starting with the left side:
1. Distribute \(2\) in the term \(2(x - 9)\):
\[
3x + 2x - 18
\]
Combining like terms:
\[
5x - 18
\]
Now the left side becomes:
\[
5x - 18
\]
Now for the right side:
1. Combine like terms:
\[
8x + x - 14 = 9x - 14
\]
Now we have the simplified equation:
\[
5x - 18 = 9x - 14
\]
Next, we'll isolate \(x\) by getting all terms involving \(x\) on one side and the constant terms on the other:
1. Subtract \(5x\) from both sides:
\[
-18 = 9x - 5x - 14
\]
This simplifies to:
\[
-18 = 4x - 14
\]
2. Add \(14\) to both sides:
\[
-18 + 14 = 4x
\]
This simplifies to:
\[
-4 = 4x
\]
3. Divide both sides by \(4\):
\[
x = -1
\]
Thus, the solution to the equation is:
\[
\boxed{-1}
\]
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