Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
To solve the equation 11x = 3(7x - 1) - 10x, first distribute the 3 to the terms inside the parentheses:
11x = 21x - 3 - 10x
Combine like terms:
11x = 11x - 3
Subtract 11x from both sides:
0 = -3
This equation is not true, so it has no solution.
The correct response is:
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(1 point)
Responses
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
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 infinite solutions.
To solve the equation 5(2x+2) - 4 = 2x + 6, first distribute the 5 to the terms inside the parentheses:
10x + 10 - 4 = 2x + 6
Combine like terms:
10x + 6 = 2x + 6
Subtract 2x from both sides:
8x + 6 = 6
Subtract 6 from both sides:
8x = 0
Divide both sides by 8:
x = 0
The equation has one solution: x = 0.
The correct response is:
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, first combine like terms:
6x + 8 = 32
Next, subtract 8 from both sides of the equation:
6x = 24
To isolate x, divide both sides by 6:
x = 4
To check whether the solution is correct, substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides are equal, we have confirmed that the solution x = 4 is correct.
The solution to the equation is x = 4.
Which of the following sentences demonstrates subject-verb agreement?(1 point)
Responses
The cat jump over the fence.
The cat jump over the fence.
The cats jumps over the fence.
The cats jumps over the fence.
The cat jumps over the fence.
The cat jumps over the fence.
The cats jumps over the fence.
The correct sentence that demonstrates subject-verb agreement is:
The cat jumps over the fence.
Which two of the following is an example of a gerund phrase?(1 point)
Responses
Running in the park
Running in the park
The broken vase
The broken vase
Surprised by the news
Surprised by the news
Holding the trophy
The two examples of a gerund phrase are:
Running in the park
Holding the trophy
Which of the following is an example of a participle phrase?(1 point)
Responses
Reading books
Reading books
The broken vase
The broken vase
His passion for singing
His passion for singing
Standing by the tree