Solving Linear Equations Online Practice

Question

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12 of 1512 of 15 Items

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: \(x = 1\).