Solve for the Variable
Solve: 5x + 2 = 3x + 8
x = 3
Two phone plans: Plan A is $30 plus $0.10/text. Plan B is $20 plus $0.15/text. At how many texts (t) do they cost the same?
t = 200 texts
Write the equation: A number (x) times 3 plus 5 is equal to the same number plus 9.
3x + 5 = x + 9
Solve: 0.5x + 3 = 0.2x + 6
x = 10
What is the first step to solve 8x - 4 = 3x + 6?
Move variable terms to one side (e.g., subtract 3x from both sides)
Solve: 7a - 10 = 2a + 5
a = 3
A car rental company charges $40 plus $0.25/mile. A second company charges $55 plus $0.20/mile. For how many miles (m) is the cost equal?
m = 300 miles
Write the equation: The perimeter of a square with side length (s + 2) is equal to the perimeter of an equilateral triangle with side length (2s).
4(s + 2) = 3(2s)
Solve: (1/2)y + 4 = (1/4)y + 5
y = 4
Find the error: 5x + 10 = 2x - 2 -> 3x = 12
Should be 3x = -12 (subtracted 10 from -2 incorrectly)
Solve: 4n + 3 = 10n - 21
n = 4
Sam has $150 and saves $10/week. Ben has $200 and saves $5/week. After how many weeks (w) will they have the same amount?
w = 10 weeks
Write the equation: A movie club costs $10 plus $2 per movie (m). A streaming service costs $20 and movies are $1 each. When is the cost the same?
10 + 2m = 20 + m
Solve: 2.5a - 8 = 1.5a + 2
a = 10
Solve: 3(x + 2) = 2x + 11
x = 5
Solve: -2y + 15 = 3y - 5
y = 4
One gym charges a $50 sign-up fee and $25/month. Another charges a $90 sign-up fee and $15/month. After how many months (m) is the total cost the same?
m = 4 months
rite the equation: A rectangle's length is 5 more than its width (w). Another rectangle's length is 1 less than twice its width. If their lengths are equal, what's the equation?
w + 5 = 2w - 1
Solve: (2/3)n - 1 = (1/3)n + 7
n = 24
If 5x + 1 = 3x + 7, what is the value of 10x?
x = 3, so 10x = 30
Solve: 6 + 4b = -10b - 8
b = -1
A plumber charges $75 for a house call plus $50/hour. An electrician charges $100 for a house call plus $45/hour. After how many hours (h) is the total bill the same?
h = 5 hours
Write the equation: A full 500-gallon tank is draining at 10 gal/min. A 100-gallon tank is filling at 6 gal/min. When is the water level (g) the same?
500 - 10g = 100 + 6g
Solve: 1.2b + 2.4 = 3.6b - 7.2
b = 4
Solve: 2(a + 4) - 3 = 3(a - 1)
a = 8