Solving Algebraic Equations
x + 5 = 8
x = 3
Solve the equation. Your answer needs to be in simplest form: x + 1/10 = 3/10
x = 1/5
Caleb is x years old. His sister is 10 years older than he is. If his sister is y years old, what is the linear equation that relates their two ages?
y = x + 10
A bag of tomatoes weighs more than 5 pounds. In terms of x, what is the inequality for this problem?
x > 5
The inequality reads: x ≥ 75. Name 3 substitutions that could be an answer for x
Answers vary (any number greater than or equal to 75)
2m = 6
m = 3
Solve the equation. Make sure your answer is in simplest form: 3y = 2/3
y = 2/9
A rhombus has sides of length r centimeters. If the perimeter of the rhombus is P centimeters, express P in terms of r.
P = 4r
Jill needs at least 7 feet of ribbon for her crafts project. In terms of j, what is the inequality that represents this problem?
j ≥ 7
The inequality reads: w ≤ -3. Name 3 possible substitutions that would make the inequality true.
Answers vary (any number than is less than or equal to -3)
26 = g + 11
g = 15
Solve the equation. Make sure your answer is in simplest form: p = 6/10 + 2/10
p = 4/5
Hannah took p minutes to jog around a park. Sofia took 12 minutes longer to jog around the park. If Sofia took t minutes to jog around the park, express t in terms of p.
t = p + 12
The maximum number of shirts Sara can buy is 9. In terms of s, what is the inequality that represents this problem?
s ≤ 9
n is an even number:
6 > n > 2
What number is n?
n = 4
12 = m/7
m = 84
Solve the equation. Make sure your answer is in simplest form: g + 5/3 = 3 2/3
g = 2
The area of Hank's farm is n acres. The area of Hank's farm is 8 times as large as the area of Stan's farm. If s represents the area of Stan's farm, express s in terms of n.
s = n/8
In the inequality, o ≤ 24.3, o represents the possible weights of a package. Is 24.4 a possible value of o?
No, o has a maximum value of 24.3
Which weighs more: 16 ounces of soda or 1 pound of solid gold?
They both weigh the same! 16 ounces = 1 pound
56x = 1400
x = 25
Solve the equation. Make sure your answer is in simplest form: 4/3y = 36
h = 27
Ethan scored x points in a game. His sister scored 8 points when she played the same game. Their combined score was y points.
y = x + 8
In the inequality, x > 9, x represents the number of restaurants along the street. Is 9 a possible value of x?
No, because x is more than 9
What can you put in between a 7 and 8, so that the result is greater than 7, but less than 8?
A decimal point