12x+5=10x−11
To solve the equation, we want to isolate the variable x on one side of the equation.
First, we can simplify both sides by combining like terms.
Starting with the left side:
12x + 5
Next, let's simplify the right side:
10x - 11
Now, we can set the two sides equal to each other:
12x + 5 = 10x - 11
To isolate the variable x, we need to move all terms containing x to one side of the equation.
Let's start by moving the 10x term to the left side by subtracting 10x from both sides:
12x - 10x + 5 = -11
Simplifying, we have:
2x + 5 = -11
Next, we can move the constant term 5 to the right side by subtracting 5 from both sides:
2x + 5 - 5 = -11 - 5
Simplifying, we have:
2x = -16
Finally, to solve for x, we divide both sides of the equation by 2:
(2x)/2 = -16/2
Simplifying, we have:
x = -8
Therefore, the solution to the equation 12x + 5 = 10x - 11 is x = -8.
At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(1 point)
To represent the number of days it would take for the two songs to have the same number of listens, let's use the variable x.
For the first song, the number of listens after x days can be represented as: 1,000 + 38x.
(Starting number of listens + new listens per day multiplied by the number of days)
For the second song, the number of listens after x days can be represented as: 900 + 40x.
(Starting number of listens + new listens per day multiplied by the number of days)
We want to find the number of days when the number of listens for both songs is equal. Therefore, we can set the two equations equal to each other:
1,000 + 38x = 900 + 40x
The equation to represent the number of days it would take for the two songs to have the same number of listens is:
1,000 + 38x = 900 + 40x
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=8
10 x equals 32 plus 6 x ; x equals 8
10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2
10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3
10x=32+6x ; x=4
To find the number of visits it would take for the cost of the two plans to be equal, we can set up an equation.
Let x represent the number of visits.
For the first option:
Cost = $10 per visit
For the second option:
Cost = $32 per month + $6 per visit
Setting up the equation:
10x = 32 + 6x
To solve for x, we can subtract 6x from both sides of the equation:
10x - 6x = 32
Simplifying:
4x = 32
To isolate x, we divide both sides of the equation by 4:
(4x)/4 = 32/4
Simplifying:
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)
The songs will have the same number of listens after
days.
To determine when the two songs will have the same number of listens, let's use the variable x to represent the number of days.
For the first song:
Number of listens = 700 + 52x (Starting number of listens + new listens per day multiplied by the number of days)
For the second song:
Number of listens = 600 + 56x (Starting number of listens + new listens per day multiplied by the number of days)
We want to find when the number of listens for both songs is equal. Therefore, we can set the two equations equal to each other:
700 + 52x = 600 + 56x
To solve for x, we can subtract 600 from both sides of the equation:
700 - 600 + 52x = 600 - 600 + 56x
Simplifying:
100 + 52x = 56x
Next, we can subtract 52x from both sides of the equation to isolate x:
100 + 52x - 52x = 56x - 52x
Simplifying:
100 = 4x
To solve for x, we divide both sides of the equation by 4:
(100) / 4 = (4x) / 4
Simplifying:
25 = x
Therefore, the two songs will have the same number of listens after 25 days.
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.
To find when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation.
Let x represent the number of weeks.
For Miguel's car:
Amount of gas used = 1.5 gallons per week
For Christina's car:
Amount of gas used = 1 gallon per week
Setting up the equation:
20 - 1.5x = 16 - 1x
To solve for x, we can subtract 16 from both sides and add 1.5x to both sides:
20 - 16 - 1.5x + 1.5x = 16 - 16 + 1x + 1.5x
Simplifying:
4 = 0.5x
To isolate x, we divide both sides of the equation by 0.5:
(4) / 0.5 = (0.5x) / 0.5
Simplifying:
8 = x
Therefore, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.
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