Solving linear & quadratic equations

#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!!!