Equations
3x - 14 = - 5
x = 3
Wanda donated 4 boxes of cans and 3 more that didn't fit in a box. The total number of cans was 51. Write and solve an equation to find the number of cans in each box.
4c + 3 = 51
c = 12 cans in each box
Determine if the following has one, no or infinite solutions.
5x + 3 = 5x - 3
No Solutions
Graph the inequality n < -1
Open circle on -1 and ray going towards the left.
You rent a moving truck for a daily fee of $20 and are charged $0.75 per mile. You budgeted a maximum total cost of $65. Write and solve an inequality that represents the number of miles (m) you can drive the truck.
20 + 0.75m < or equal to 65
m < or equal to 46.7 miles
So 46 miles
Find the value of x that makes the equation true.
5 - 2(x + 3) = 15
-8
Imani spent half of her weekly allowance playing mini-golf. To earn more money her parents let her wash the car for $4. What is her weekly allowance if she ended with $12?
1/2a + 4 = 12
a = $16
Determine whether the equation has one, no or inifinite solutions.
8(4 - 2x) = 4(3 - 5x) + 4x
No Solutions
Graph the inequality for 5 < x
Open circle on 5. Arrow/Ray going towards the right.
You need at least 5000 points to level up on your video game. You currently have 2700 points. Write and solve an inequality that represents the number of points (p) you still need to level up.
p > or equal to 2300
so 2300 or more
Solve. 6n - 1 = 4n - 5
n = -2
A car rental company charges a flat fee of $30 per day plus $0.20 per mile driven. If Jane rented a car and was charged $70, how many miles did she drive?
30 + 0.20m = 70
m = 200 miles
What numbers would complete the equation so that it has infinitely many solutions?
6x - x + 4 + 2x = ____x + ____
7x + 4
Solve.
3n + 19 > 28
n > 3
A cell phone company charges $35 per month for an unlimited data plan and charges a one time $100 activation fee. Your parents will only spend a maximum of $485 on your phone plan. Write and solve an inequality that represents the total months (m) your parents will pay for the phone plan.
35m + 100 < or equal to 485
m < 11 months
so, 11 months is the maximum number of months they will pay for the plan
Solve.
-8m - m = -3(2m - 4) + 3m
m = -2
Green's Gym charges a one time fee of $50 plus $30 per session for a personal trainer. Breakout Gym charges an annual fee of $250 plus $10 per session with a trainer. For how many sessions is the cost of the two plans the same? Write and solve an equation.
50 + 30x = 250 + 10x
x = 10 sessions
Complete the equation with values that will result in an equation with no solution.
3(2x + 4) - x = ____x + ____
4x +/- any number other than +12
Solve.
-2.45x + 3.2 < -6.6
x > 4
A convenience store requires you to spend at least $6 in order to use a debit card. You want to buy a bottle of OJ for $1.20. Donuts cost $0.80 each. Write and solve an inequality that represents the amount of donuts (d) you can purchase in order to meet the debit card requirement.
1.20 + 0.80d > or equal to 6
d > or equal to 6
so 6 or more donuts must be purchased to meet the debit card requirement
Solve.
-5(2x + 3) - x = 4(x + 11) + 1
x = -4
Annie is comparing the cost to ship a package. One shipping company charges $7 for the first pound and $0.20 for each additional pound. Another shipping company charges $5 for the firs pound and $0.30 for each additional pound. Write and solve an equation that could be used to determine the number of pounds when the cost would be the same.
7 + 0.20x = 5 + 0.30x
x = 20 pounds
Which equation has no solution?
a. 5(b + 3) - 2b = 2b + 3
b. 4(d - 3) + 5 = 3(d + 2) - 7
c. 3(x + 5) = 5(x + 3) - 2x
d. -10y + 18 = -3(5y - 7) + 5y
d. -10y + 18 = -3(5y - 7) + 5y
6(x - 5) > 3(x - 1)
x > 9
A video streaming company offers two monthly plans. Plan A: $3 per video viewed, plus a flat rate of $8 per month Plan B: $5 per video viewed and no additional flat rate
Write and solve an inequality to determine when the cost of viewing n videos using Plan A is less than the cost of viewing n videos using Plan B.
3v + 8 < 5v
v > 4 , so they would need to rent 5 videos