Solve for x to determine if the equation has one, none, or infinite solutions.

11x=3(7x−1)−10x

A. The equation has one solution: x=−1.

B. The equation has one solution: x=−3.

C. The equation has no solution.

D. The equation has infinite solutions.

7 answers

First, we simplify the equation:

11x = 3(7x-1) - 10x
11x = 21x - 3 - 10x
11x = 11x - 3

Now, subtract 11x from both sides:

0 = -3

Since this equation leads to a false statement, there are no solutions. Therefore, the answer is:

C. The equation has no solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6

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

B. The equation has infinite solutions.

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

D. The equation has no solution.
First, simplify the equation:

5(2x + 2) - 4 = 2x + 6
10x + 10 - 4 = 2x + 6
10x + 6 = 2x + 6

Subtract 2x from both sides:

8x + 6 = 6

Now, subtract 6 from both sides:

8x = 0

Dividing both sides by 8:

x = 0

Therefore, the equation has exactly one solution, x = 0. The correct answer is:

A. The equation has one solution: x=0.
Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x + 8 + x = 32
To solve the equation 5x + 8 + x = 32, we first combine like terms on the left side:

5x + 8 + x = 32
6x + 8 = 32

Next, we isolate the variable by subtracting 8 from both sides:

6x + 8 - 8 = 32 - 8
6x = 24

Now, we solve for x by dividing both sides by 6:

6x / 6 = 24 / 6
x = 4

Now that our solution is x = 4, we can check our answer by substituting x back into the original equation:

5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32

Since the left side equals the right side, our solution x = 4 is correct.
Explain in 1-2 sentences please.
To solve the equation 5x + 8 + x = 32, we combined like terms to simplify the left side of the equation. By isolating the variable x, we determined that x = 4 is the solution. Substituting x back into the original equation confirmed that x = 4 satisfies the equation, verifying our solution.