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.
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
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.
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.
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
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.
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.