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Solving Equations That Require Multiple Steps
Part One
So far this unit we have solved equations in algebra that have only required one step to solve.
Example : Solve x + 4 = 8
- we subtract 4 from each side and get x = 4
Now, we will be solving larger equations that need more than just one step.
SAMDEB - or reverse BEDMAS - is a quick way to remember how to solve multi-step problems.
This means we have to solve these equations by doing the addition/subtraction step first and the
exponents or brackets last.
Example :
Solve 2x + 4 = 12
Solution :
2x + 4 - 4 = 12 - 4 (subtract first)
2x = 8 (what we get after subtracting)
2x ÷ 2 = 4 ÷ 2 (divide next)
x=2
Sometimes we have to do other steps before we start solving the problem, like combining like terms or
use the distributive property. This will prepare all the variables and terms for us to work with.
** Try your best to put variables on one side of the equation and numbers on the other side of the equation.
Example :
Solve 4z + 3 = 7z - 9
Solution :
4z + 3 + 9 = 7z - 9 + 9 (get rid of the - 9 bu adding 9 to each side)
4z + 12 = 7z (the 9 on the right becomes zero and the numbers on the left add to 12)
4z + 12 - 4z = 7z - 4z (get rid of the 4z on the left side by subtracting it from both sides)
12 = 3z (the 4z on the left becomes zero and the z’s on the right become 3z)
12 ÷3 = 3z ÷3 (divide both sides by 3 since the 3z is multiplication)
4 = z (12 divided by 3 is 4 and 3 divided by 3 becomes one)
Homework Questions:
Solve the following and show all the steps you used:
a) 5x + 4 = 34
b) 6y + 3 = 45
c) 8d - 7 = 57
d) 3f + 4 = 22 – 3
e) 4x + 2 = 14
f) 8u - 13 = 3
g) 54 = 12g + 6
h) 8w ÷ 3 = 8
i) 22 - 3x = x - 10