Question

Solving Linear Equations Online Practice
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Question
Solve for x
to determine if the equation has one, none, or infinite solutions.
3(2x+2)−4=−2x+10
(1 point)
Responses

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has no solution.
The equation has no solution.

The equation has one solution: x=1
.
The equation has one solution: x equals 1 .

The equation has infinite solutions.

Answer 1

To solve the equation \(3(2x+2) - 4 = -2x + 10\), we can follow these steps:

1. **Distribute the 3 on the left side:**
\[
6x + 6 - 4 = -2x + 10
\]
Simplifying the left side gives:
\[
6x + 2 = -2x + 10
\]

2. **Add \(2x\) to both sides:**
\[
6x + 2x + 2 = 10
\]
This simplifies to:
\[
8x + 2 = 10
\]

3. **Subtract 2 from both sides:**
\[
8x = 10 - 2
\]
Simplifying gives:
\[
8x = 8
\]

4. **Divide both sides by 8:**
\[
x = 1
\]

Now, let's determine the nature of the solution:
- Since we found \(x = 1\), the equation has **one solution**.

**The answer is:**
The equation has one solution: \(x = 1\).