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 infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has no solution.
To solve for x, we first simplify the expression on the right side of the equation:
3(7x-1) - 10x
= 21x - 3 - 10x
= 11x - 3
Now, we substitute this back into the original equation:
11x = 11x - 3
Next, we isolate x by subtracting 11x from both sides:
0 = -3
Since this equation is false (0 does not equal -3), there are no solutions to the equation. Therefore, 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 infinite solutions.
The equation has infinite solutions.
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.
To solve for x, we first distribute the 5 on the left side of the equation:
5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6
Now, the equation becomes:
10x + 6 = 2x + 6
Next, we subtract 2x from both sides to isolate x:
10x - 2x + 6 = 6
8x + 6 = 6
Subtracting 6 from both sides, we get:
8x = 0
Dividing by 8 on both sides gives:
x = 0
Therefore, 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, we first combine like terms on the left side:
5x + x + 8 = 32
6x + 8 = 32
Next, we subtract 8 from both sides to isolate the variable term:
6x = 32 - 8
6x = 24
Then, we divide by 6 on both sides to solve for x:
x = 24/6
x = 4
To check our answer, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides are equal, the solution x = 4 is correct.
Therefore, the solution is x = 4 and it has been checked.