One-step Linear Equations (Addition/Subtraction)
j + 12 = 14
What is j?
j = 2
Steps:
j + 12 - 12 = 14 - 12
j = 2
5j = 125
What is j?
j = 25
Steps:
5j /5 = 125 /5
j = 25
5c = 22 + 3
What is c?
c = 5
Steps:
5c = 25
5c / 5 = 25/5
c = 5
Ushieja needs to solve the equation c + 22 = 56 to find the cost, c, of taking a car on the ferry from Vancouver to Victoria. What is the cost? (Show your solution)
c = 34
Steps:
c + 22 - 22 = 56 - 22
c = 34
17 = d - 9
What is d?
d = 26
Steps:
17 + 9 = d - 9 + 9
26 = d
9 = m/6
What is m?
m = 54
Steps:
9 x 6 = m/6 x 6
54 = m
4 + 9g = 22
What is g?
g = 2
Steps:
4 - 4 + 9g = 22 - 4
9g = 18;
9g/9 = 18/9
g = 2
Asahi is one-half Dylan’s age. Asahi is 21. Write an equation for this situation and tell how old Dylan is? (Show your solution)
Equation: d/2 = 21
Dylan is 42 years old
Steps:
d/2 x 2 = 21 x 2
d = 42
15 - y = 5
What is y?
y = 10
Steps:
15 - y + y = 5 + y
15 = 5 + y;
15 - 5 = 5 - 5 + y
10 = y
x/2 = 0
What is x?
x = 0
Steps:
x/2 x 2 = 0 x 2
x = 0
29 = 12n + 5
What is n?
n = 2
Steps:
29 - 5 = 12n + 5 - 5
24 = 12n;
24/12 = 12n/12
2 = n
Mr. Kamal is saving for a new watch that costs $1485. He needs triple his savings before he has enough money for the fancy new watch he wants to buy. Write an equation for this situation and tell how much money has Mr. Kamal saved so far? (show your solution)
a = $495
Steps:
3a/3 = 1485/3
a = 495
Is x = 5 a solution to the equation:
37 = 42 - x ?
(Show your solution)
Yes. x = 5 is a solution.
Steps:
37 + x = 42 - x + x
37 + x = 42;
37 - 37 + x = 42 - 37
x = 5
Is x = 3 a solution to the equation:
32x = 96 ?
(Show your solution)
Yes! x = 3 is a solution.
Steps:
32x / 32 = 96 / 32
x = 3
Is x = 3 a solution to the equation:
14 = 4n - 2 ?
(Show your solution)
No! It x=3 is not a solution.
Steps:
14 + 2 = 4n - 2 + 2
16 = 4n;
16/4 = 4n/4
4 = n
Matt sees an advertisement that says “Buy one box of cereal and get a 1-L carton of milk for $1!”
Matt pays $10 for two boxes of cereal and two 1-L cartons of milk. Write the equation and tell what is the price of one box of cereal? (show your solution)
Equation: 2c + 2 =10
c = $4
Steps:
1 carton of milk for 1 dollar if 1 cereal box. Since Matt bought 2, he got 2 cartons for 2 dollars.
Price of 2 cereal boxes = 2c
Price of cereal boxex + price of milk cartons = 10
2c + 2 = 10;
2c + 2 - 2 = 10 - 2
2c = 8;
2c/2 = 8/4
c = 4
Checking answer
LHS: 2(4) + 2 = 10
RHS: 10
Answer is correct
The sum of a 3 and a number is 11. What is the number?
The number is 8!
Steps:
3 + n = 11;
3 - 3 + n = 11 - 3
n = 8
One-quarter of a number equals 8. What is the number?
The number is 32!
Steps:
n/4 = 8;
n/4 x 4 = 8 x 4
n = 32
2 subtracted from 6 times a number is 16. What is the number?
The number is 3!
Steps:
6t - 2 = 16;
6t - 2 + 2 = 16 + 2
6t = 18;
6t/6 = 18/6
t = 3
The food energy credits required by a steeplechase racer in a video game can be modelled with the formula E = 3520 + 25T, where E represents the amount of food energy, in calories, and T represents the simulated air temperature, in degrees Celsius. At what temperature does the racer require 4095 calories of food energy? (show your solution)
T = 23 degree Celsius
Steps:
E = 4095 calories
Equation: E = 3520 + 25T
put in 4095 for "E"
4095 = 3520 + 25T;
4095 - 3520 = 3520 - 3520 + 25T
575 = 25T;
575/25 = 25T/25
23 = T