Equations & Formulas
Solve: 4x − 3 = 17
x = 5
The sum of three consecutive integers is 48. Find them.
15, 16, 17
How many cents are 6 nickels and 4 dimes worth?
70 cents
Solve: x + 7 > 12
x > 5
Solve: |x| = 5
x = 5 or x = −5
Solve: (3/4)x − 2 = 10
x = 16
After 20% off, a shirt costs $36. What was the original price?
$45
8 lb of $3/lb candy is mixed with 2 lb of $8/lb candy. What is the price per pound of the mix?
$4 per pound
Solve: −3x ≤ 18
x ≥ −6 (the sign flips)
Solve: |x + 2| = 6
x = 4 or x = −8
Solve P = 2L + 2W for L.
L = (P − 2W)/2
A rectangle’s length is 4 more than its width. The perimeter is 40. Find the length and width.
Width 8, length 12
Two cars leave the same place in opposite directions at 50 mph and 60 mph. How many hours until they are 330 miles apart?
3 hours
A phone plan costs $25 plus $5 per GB. Your budget is at most $60. What is the greatest number of whole GB you can use?
7 GB (25 + 5g ≤ 60, so g ≤ 7)
Solve: |x − 1| < 4
−3 < x < 5
Solve 2x − 5y = 10 for y.
y = (2x − 10)/5, or y = (2/5)x − 2
One number is 5 less than 3 times another. Their sum is 31. Find both numbers.
9 and 22
Tom leaves at 30 mph. Two hours later Ann leaves the same way at 50 mph. How many hours after Ann leaves does she catch Tom?
3 hours
Solve: 1 < 2x + 3 < 9
−1 < x < 3
Solve: |x − 3| + 2 = 9
x = 10 or x = −4
5(x − 1) = 5x + 3. How many solutions?
No solution (the equation simplifies to −5 = 3)
Jan has 3 times as many stickers as Leo. After Jan gives 6 to Leo, they have the same number. How many did Jan start with?
18 (Leo started with 6)
How many pounds of $4/lb nuts must be mixed with 10 lb of $7/lb nuts to make a mix worth $5/lb?
20 pounds
Solve: 3x − 1 < 5 or 2x + 1 > 9. Write in interval notation.
(−∞, 2) ∪ (4, ∞)
Solve: |2x − 1| ≥ 7
x ≤ −3 or x ≥ 4