Solving For One Variable
Is it a solution?
Equivalent Equations
Graph That
Writing Equations
100
Solve the following equation for x:
x/3-1=4
x=15
100
Is 2 a solution to the following equation:
5x = 10?
Explain or show how you know.
Yes
5(2) = 10
100
Is 2x - 4 = 12 equivalent to 2x + 4 = 12? Explain or show your reasoning.
No
100
The following graph represents the relationship between water in a tank and time. How much water is left in the tank after 10 minutes?
250 gallons
100
A pound of grapes costs $3. Write an equation that represents the relationship between p pounds of grapes and T, the total cost.
3p = T or
3*p=t
200
Solve the equation below for b:
g=b-5
g+5=b
b=g+5
200
Solve the following equation for x:
2x+7=27
x = 10
200
Is 3x-5=10 equivalent to 3x=5? Show or explain your reasoning.
No, you do not do the same thing to both sides to get from one to the other.
200
The graph below shows the relationship between the amount of money in a student's savings account and the number of weeks since the student started depositing money.
What does the point (20, 3000) mean in this context?
The student has $3,000 dollars in their bank account after 20 weeks.
200
A group of students is volunteering to help clean up a 3-mile stretch of road. The students want to split up that 3 mile stretch evenly so that each student is cleaning up the same amount of road. If there are n students, write an equation we could use to find the amount of road each student is cleaning up.
3/n
300
Solve the equation below for y. Be sure to simplify your answer.
3x+2y=6
y=(6-3x)/2
300
Is x = 5 and y = -2 a solution to the following equation?
3y-5x = -30
No, 3(-2) - 5(5) = -31
300
Are the equations 4x - 0.5 = 7 and 8x = 15 equivalent? Show or explain your reasoning
Yes, if we solve for x in the first equation, we get x=1.875 and we also get this if we solve for x in the second equation.
300
Is (2, -2) a solution to the equation graphed below? Explain your reasoning
Yes, it is on the graph.
300
The cost of making t-shirts at Shirt Company is $7 per shirt plus a $9 shipping charge. Write an equation that represents the relationship between s, the number of shirts, and c, the total cost of making the t-shirts.
7s + 9 = c
400
Solve the following equation for x
2f-3x=g
x=(g-2f)/-3
400
Is x = 2.5 and y = 3 a solution to the following equation? 2x+3y-4 =10
Explain/show how you know
Yes, 2(2.5) + 3(3) - 4 = 10
400
Are the equations 3x + 2y = 6 and 6x + 4y = 12 equivalent? Explain or show your reasoning.
Yes, just multiply both sides of the first equation by 2 to get the second equation
400
Below is the graph of 2x + y = 2. Is the point (4,1) a solution to this equation? Explain your reasoning.
No, it is not on the line of the graph.
400
A group of students is raising money for the wrestling team. The students plan to raise a total of $1500 for their team, and they plan on splitting up the $1500 so that each person raises an equal amount. Write an equation that shows the relationship between n, the number of students, and a, the amount each students needs to raise.
1500/n = a
or 1500 ÷ n = a
500
The equation L = 400 - 1.5m represents the relationship between liters in a tank of water and minutes. Rewrite the equation by solving for m.
m = (400 - L)/1.5
m = (L - 400)/-1.5
500
The following equation represents the relationship between calories from protein and fat in a snack:
4p + 9f = 95
Is p = 3.5 grams and f = 9 grams a solution?
Yes
4(3.5) + 9(9) = 95
500
Is 2x + 4y = 10 equivalent to the equation below? Show or explain your reasoning.
y = (10-2x)/4
Yes, if we solve the first equation for y we will get the second equation.
500
The graph below shows the total cost of ordering different amounts of hats from an online hat store. Identify a point that is a solution to the graph below and explain what it means in this situation.
Example: (6, 120) which would mean 6 hats cost $120
500
A tank with 150 liters in it drains at a rate of 3.5 liters a minute. Write an equation to represent the relationship between L, the water left in the tank, and m, the number of minutes.
150 - 3.5m = L