Solve for x
to determine if the equation has one, none, or infinite solutions.
3(2x+2)−4=−2x+10
3(2x + 2) - 4 = -2x + 10
Simplify the equation:
6x + 6 - 4 = -2x + 10
Combine like terms:
6x + 2 = -2x + 10
Add 2x to both sides:
8x + 2 = 10
Subtract 2 from both sides:
8x = 8
Divide both sides by 8:
x = 1
Therefore, the equation has one solution.
To solve the equation 3(2x+2)−4=−2x+10, let's follow these steps:
Step 1: Distribute the 3 to the terms inside the parentheses:
6x + 6 - 4 = -2x + 10
Step 2: Combine like terms on both sides of the equation:
6x + 2 = -2x + 10
Step 3: Add 2x to both sides of the equation to eliminate the -2x term on the right side:
6x + 2 + 2x = -2x + 10 + 2x
8x + 2 = 10
Step 4: Subtract 2 from both sides to isolate the x variable on the left side:
8x + 2 - 2 = 10 - 2
8x = 8
Step 5: Divide both sides by 8 to solve for x:
(8x) / 8 = 8 / 8
x = 1
Therefore, the equation has only one solution, which is x = 1.