Solving Equations
Aim: How can we solve for x in an equation?
Do Now:
Simplify:
1)  2(6 x 4  3x 3  5x 2  x  7)  3( x 4  2 x 3  x 2  8)
2) 3x( xy  4)  4( x 2 y  2 y)
To find the root of an equation (or “finding x”), we must isolate x on one side of the
equation.
IMPORTANT TO REMEMBER: What you do to one side of the equation, you must
do to the other!
Solving Single-Step Equations:
We must use inverse operations in order to get x alone on the left side.
Def: Inverse operations are opposite operations, for example, addition and subtraction.
Ex: X + 7 = 23
-7 -7
X = 16
The opposite of addition: ____________________
The opposite of multiplication: _______________
Ex:
1) x + 3 = 10
2) 17 + x = 38
5) 12  x  51
3) 6x = 48
4)
1
x  12
4
Solving Multi-Step Equations:
We must work in the opposite order of PEMDAS because we are using inverse
operations.
Ex: 2x + 7 = 23
-7 -7
2x = 16
2
2
X=8
To check if the root is correct, plug the value of x into the original equation and solve.
Ex: Solve and check:
1) 3x – 7 = 23
5) 6 
2)
1
x23
4
3) 3(x – 2) = 18
4) 21 – 4x = 57
4
x  26
5
Equations with more than one x on one side:
Combine like terms and solve the single or multi-step equation.
3
1
6  x  ( x  4)
Ex: -6x + 4x = 2
2
2
Ex:
3
1) 3x  (2 x  1)  2
2) 55x – 3(9x + 12) = -64
3) 2x + 5x – 11 = 10
2
4) 7(4x - 5) - 4(6x + 5) = -91
5) 9(3x + 6) - 6(7x - 3) = 12
Solving Equations with Variables on Both Sides:
Step 1: Isolate all x’s on one side of the equation and all numbers on the other.
Step 2: Combine like terms.
Step 3: Solve for x.
Ex: 7x + 19 = -2x + 55
+2
+2
9x + 19 = 55
- 19 - 19
9x = 36
9
9
X=4
Ex:
1) 8y + 14 = 6y
4) 9(b – 4) = 5(3b – 2)
2) -7 + 4m = 6m – 5
1
5) (8n  2)  16  30n
2
Homework: Workbook pg. 46, 25-30; pg. 50, 36-44
3) 6(3 – x) = 3x
6) 3x - 25 = 11x - 5 + 2x