#SOLVED NA ‘KO!
Solving Linear & Quadratic Equations
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Throughout Algebra, you will hear many different terms being used to describe the parts of an equation or expression.
You will need to know the definition of the following terms throughout the course.
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Variable:A letter which is used to represent an unknown number or value.
Any letter can be used as a variable.
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Coefficient: The number in front of a
variable in a mathematical equation or expression.
The coefficient is actually being multiplied by the variable
x3 Coefficient: 3Means: 3 times x
2
4
1x Coefficient: ¼
Means: ¼ times x2
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Constant:A number being added or subtracted from a variable in an equation or expression.
95 x
The constant in the above expression is: -9
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Expression:Contains at least one variable.
Examples: a5xzy 23
Review of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Equation:A sentence that states that two mathematical expressions are equal.
Examples:
2253 x
hrV 2174132 xx
Steps to Solving Linear Equations
1. Simplify each side of the equation, if needed, by distributing or combining like terms.
2. Move variables to one side of the equation by using the opposite operation of addition or subtraction.
3. Isolate the variable by applying the opposite operation to each side.a. First, use the opposite operation of addition or
subtraction. b. Second, use the opposite operation of multiplication or
division.
4. Check your answer.
Example X – 5 = 4
X – 5 + 5 = 4 + 5
X = 9
Example X – 7 = 13
X – 7 + 7 = 13 + 7
X = 20
Example 2X – 3 = 7
2X – 3 + 3 = 7 + 3
2X = 102 2
X = 5
Example 5X + 4 = 9
5X + 4 - 4 = 9 - 4
5X = 55 5
X = 1
Simplify: Use the distributive property
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
Simplify: Combine like terms
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
30)122()155( xx
Isolate Variables: Undo the addition
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
30)122()155( xx
3033 x
Isolate Variables: Undo the multiplication
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
30)122()155( xx
3033 x273 x
Check your answer: Substitute the value of x back in
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
30)122()155( xx
3033 x
9x273 x
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
30)6(2)3(5 xxEXAMPLE:
30)69(2)39(5 30)15(2)12(5
303060 3030
The answer is true; therefore, the vale of x is true.
Simplify: Use the distributive property
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
Move Variables: Move the -15x to the other side of the equation.
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
631515 xx
Isolate Variables: Undo the addition
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
631515 xx
61815 x
Isolate Variables: Undo the multiplication
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
631515 xx
61815 xx189
Check your answer: Substitute the value of x back in
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
631515 xx
61815 xx189
x2
1
The answer is true; therefore, the vale of x is true.
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
)2(3)1(15 xxEXAMPLE:
2
2
13
2
1115
2
53
2
115
2
15
2
15
Isolate Variables: Undo the addition
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
1375
2x
EXAMPLE:
Isolate Variables: Undo the division
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
EXAMPLE:
1375
2x
65
2x
Isolate Variables: Undo the multiplication
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
EXAMPLE:
1375
2x
65
2x
302 x
Check your answer: Substitute the value of x back in
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
EXAMPLE:
1375
2x
65
2x
302 x
15x
The answer is true; therefore, the vale of x is true.
STEPS TO SOLVINGSTEPS TO SOLVING:
1) Simplify
2) Move Variables
3) Isolate Variables
a. Undo addition/subtraction
b. Undo multiplication/division
4) Check your answer
EXAMPLE:
1375
2x
1375
30
1376
1313
Example
Example
2 2
STEPS TO SOLVING STEPS TO SOLVING QUADRATIC QUADRATIC EQUATIONEQUATION:
1) Equate one side to 0.
2) Factor
[solve for the zeros of the linear factors]
Or use quadratic formula
3) Check your answer
EXAMPLE:
(x +6)(x -1)x = -6 x = 1
Example
Example
Example
Example
Example
For More Practice: Solve for x
=
Solve for x:3X + 5 = 5X – 3
30 secondsTime is
up!!!
Solve for x:2x + 7 = 9x – 4
30 secondsTime is
up!!!
Solve for x:x2 + 7x = 9x – 1
30 secondsTime is
up!!!
Solve for x:2x2 + 3x = x +12
60 secondsTime is
up!!!