solving equations
Solve the following equation:
2x = 10
x=5
Solve the following inequality:
-5x < 10
x > -2
Zashary has 26 dogs. Her neighbor gave her d more dogs. She has 31 dogs in total. Using d to represent the dogs her neighbor gave her, write an equation to represent the situation.
26 + d = 31
Rona has $80 to spend at the mall. So far, she has spent $40. She now wants to buy Fidget Spinners for $5 each. Write an inequality to represent the number of Fidget Spinners she can buy.
40 + 5f ≤ 80
The formula for the area of a rectangle is A = LW. Solve the following equation for L.
L = A/W
Solve the following equation:
2x + 6 = 12
x=3
Solve the following inequality:
2x - 8 < 12
x < 10
John made $12 per delivery plus a base pay of $30. If he made $150, how many deliveries did John make? Write an equation to model the situation.
12d + 30 = 150
Tyler has a part time job. He earns $7 an hour. He can make at most $143.50 a week. What is the greatest number of hours that he can works? Using h to represent the number of hours he worked, write an inequality to model the situation.
7h ≤ 143.50
The formula for the area of a rectangle is A = LW. Solve the following equation for W.
W = A/L
Solve the following equation:
-3(x + 2) = 6
x = -4
-6(x + 1) ≤ -3
x ≥ -0.5
Davante charges $15 plus $5.50 per hour to mow lawns. Ari charges $12 plus $6.25 per hour to mow lawns. Write an equation that represents how many hours Davante and Ari will charge the same amount.
15 + 5.50h = 12 + 6.25h
Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. Write an inequality to model the situation.
22 + 8t ≤ 60
The formula for the area of a triangle is
A = 1/2bh. Solve the equation for b.
b = 2A/h
Solve the following equation:
8x - 7 = 2x +5
x = 2
Solve the following inequality:
4y - 12 ≤ 8y + 4
-4 ≤ y or y ≥ -4
UPS charges $7 for the first pound and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. Write an equation that represents how many additional pounds after the first pound will it take for UPS and FedEx to cost the same.
7 + 0.20x = 5 + 0.30x
A yellow cab taxi charges a $1.75 one-time fee in addition to $0.65 per mile. Katie has no more than $10 to spend on a ride. Write an inequality that represents Katie’s situation.
1.75 + 0.65m ≤ 10
The formula for the perimeter, P, of a triangle with sides of length a, b and c is P=a+b+c. Solve the formula for a in terms of P, b, and c.
a = P - b - c
Solve the following equation:
3(x - 1) = 9 - x
x = 3
Solve the following inequality:
4p + 2 < 2(p +5)
p < 4 or 4 > p
Two long distances phone companies are in competition. Company A charges a $40 fee plus $0.25 per minute. Company B charges a $50 fee plus $0.15 per minute.
40 + 0.25x = 50 + 0.15x
Peter has $100 to spend on drinks for his party. Bottles of lemonade cost $2 each, and juice boxes cost $0.50 each. If x is the number of bottles of lemonade and y is the number of juice boxes, which inequality models this situation?
2x + 0.50y ≤ 100
The formula for the volume of a square pyramid is V=1/3LWH. Solve for W in terms of V, L, and H.
W = 3V/LH