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 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.
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 −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.
Which of the following equations has exactly one solution?(1 point)
Responses
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
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
−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=−1.
The equation has one solution: x equals negative 1 .
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has one solution: x=−3.
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 no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=1.
The equation has one solution: x=1.
Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x+8+x=32
(4 points)
To solve the equation, let's combine like terms and isolate the variable x:
5x + 8 + x = 32
Combining like terms:
6x + 8 = 32
Next, let's isolate the variable x. We'll subtract 8 from both sides:
6x + 8 - 8 = 32 - 8
The 8s cancel out on the left side:
6x = 24
To get the value of x, we'll divide both sides of the equation by 6:
(6x)/6 = 24/6
Simplifying:
x = 4
To check if x = 4 is the correct solution, we substitute it back into the original equation and see if both sides of the equation are equal.
Original equation: 5x + 8 + x = 32
Substituting x = 4:
5(4) + 8 + 4 = 32
Simplifying:
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, the solution x = 4 is correct.
To determine when Miguel and Christina will have the same amount of gas in their tanks, we need to calculate how long it will take for both of them to use the same amount of gas.
Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week.
We can set up an equation to represent the difference in the amount of gas between Miguel and Christina over time:
20 (Miguel's tank capacity) - 1.5x = 16 (Christina's tank capacity) - 1x
Where x represents the number of weeks.
Simplifying the equation:
-1.5x + 3 = -1x + 16
Combining like terms:
-0.5x = 13
Dividing both sides by -0.5:
x = -26
Since it doesn't make sense to have a negative number of weeks, we can disregard this solution.
Therefore, the correct answer is:
After 1.6 weeks they will have the same amount of gas in their tanks.