Solve for x

Question

x
to determine if the equation has one, none, or infinite solutions.
3(2x+2)−4=−2x+10
3
(
2
x
+
2
)
−
4
=
−
2
x
+
10
(1 point)
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
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
x
=
1
.

Answer 1

To solve the equation \(3(2x+2) - 4 = -2x + 10\), let's simplify and solve step-by-step.

1. First, distribute the 3 on the left side: \[ 3(2x) + 3(2) - 4 = -2x + 10 \] \[ 6x + 6 - 4 = -2x + 10 \] \[ 6x + 2 = -2x + 10 \]

2. Next, add \(2x\) to both sides to collect the \(x\) terms: \[ 6x + 2x + 2 = 10 \] \[ 8x + 2 = 10 \]

3. Now, subtract 2 from both sides: \[ 8x = 10 - 2 \] \[ 8x = 8 \]

4. Finally, divide both sides by 8: \[ x = 1 \]

Now that we have found \(x = 1\), let's determine the nature of the solutions:

Since we have one specific solution, the equation has one solution: \(x = 1\).

So the correct response is: The equation has one solution: \(x = 1\).