An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.(1 point)
Responses
10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2
10x=32+6x ; x=8
10 x equals 32 plus 6 x ; x equals 8
10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3
10x=32+6x ; x=4
10x = 32 + 6x ; x = 4
Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point)
Responses
After 8 weeks they will have the same amount of gas in their tanks.
After 8 weeks they will have the same amount of gas in their tanks.
After −8 weeks they will have the same amount of gas in their tanks.
After negative 8 weeks they will have the same amount of gas in their tanks.
After 18 week they will have the same amount of gas in their tanks.
After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks.
After 1.6 weeks they will have the same amount of gas in their tanks.
After 1.6 weeks they will have the same amount of gas in their tanks.
We can set up an equation to solve for the number of weeks it will take for Miguel and Christina to have the same amount of gas in their tanks.
Let's say x is the number of weeks that have passed.
Miguel's gas used in x weeks: 1.5x
Christina's gas used in x weeks: 1x
Now we can set up the equation:
20 - 1.5x = 16 - 1x
Simplifying the equation:
2 = 0.5x
Dividing both sides by 0.5:
x = 4
Therefore, it will take 4 weeks for Miguel and Christina to have the same amount of gas in their tanks.
Which of the following equations has exactly one solution?(1 point)
Responses
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
−3x−8=3x−8
The equation that has exactly one solution is:
-3x - 8 = 3x - 8
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=−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.
The equation has no solution.
The equation has infinite solutions.
To solve the equation:
11x = 3(7x - 1) - 10x
Start by distributing the 3:
11x = 21x - 3 - 10x
Combine like terms:
11x = 11x - 3
Subtract 11x from both sides:
0 = -3
Since this results in a false statement (-3 = 0), there is no solution.
Therefore, 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=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
To solve the equation:
5(2x + 2) - 4 = 2x + 6
Start by distributing the 5:
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
Therefore, 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