The document provides an overview of terms and steps used to solve linear and quadratic equations. It defines variables, coefficients, constants, expressions, and equations. It then outlines the steps to solve linear equations which are: 1) simplify, 2) move variables, 3) isolate variables by undoing addition/subtraction and multiplication/division, and 4) check the answer. Examples are provided to demonstrate each step. The document also provides an overview of solving quadratic equations by factoring or using the quadratic formula. More practice problems are provided for the reader to solve.

1. #SOLVED NA ‘KO!

2. Solving Linear & Quadratic
Equations

3. 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.

4. 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.

5. 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: 3
Means: 3 times x
2
4
1
x Coefficient: ¼
Means: ¼ times x2

6. 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

7. Review
of
Terms
1) Variable
2) Coefficient
3) Constant
4) Expression
5) Equation
Expression:
Contains at least one variable.
Examples:
a
5+x
zy 23 −

8. 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 2
π=
174132 +=− xx

9. 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.

10. Example X – 5 = 4
X – 5 + 5 = 4 + 5
X = 9

11. Example X – 7 = 13
X – 7 + 7 = 13 + 7
X = 20

12. Example 2X – 3 = 7
2X – 3 + 3 = 7 + 3
2X = 10
2 2
X = 5

13. Example 5X + 4 = 9
5X + 4 - 4 = 9 - 4
5X = 5
5 5
X = 1

14. 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 =+−+ xx
EXAMPLE:

15. 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 =+−+ xx
EXAMPLE:
30)122()155( =+−+ xx

16. 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 =+−+ xx
EXAMPLE:
30)122()155( =+−+ xx
3033 =+x

17. 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 =+−+ xx
EXAMPLE:
30)122()155( =+−+ xx
3033 =+x
273 =x

18. 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 =+−+ xx
EXAMPLE:
30)122()155( =+−+ xx
3033 =+x
9=x
273 =x

19. 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 =+−+ xx
EXAMPLE:
30)69(2)39(5 =+−+
30)15(2)12(5 =−
303060 =−
3030 =
The answer is true; therefore, the
vale of x is true.

20. 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 −−−=− xx
EXAMPLE:

21. 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 −−−=− xx
EXAMPLE:
631515 +=− xx

22. 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 −−−=− xx
EXAMPLE:
631515 +=− xx
61815 += x

23. 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 −−−=− xx
EXAMPLE:
631515 +=− xx
61815 += x
x189 =

24. 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 −−−=− xx
EXAMPLE:
631515 +=− xx
61815 += x
x189 =
x=
2
1

25. 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 −−−=− xx
EXAMPLE:






−
−
−=





− 2
2
1
3
2
1
115





 −
−=





2
5
3
2
1
15
2
15
2
15
=

26. 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
137
5
2
=+x
EXAMPLE:

27. 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:
137
5
2
=+x
6
5
2
=x

28. 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:
137
5
2
=+x
6
5
2
=x
302 =x

29. 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:
137
5
2
=+x
6
5
2
=x
302 =x
15=x

30. 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:
137
5
2
=+x
137
5
30
=+
1376 =+
1313 =

31. Example

32. Example
2 2

33. STEPS TO SOLVINGSTEPS TO SOLVING
QUADRATICQUADRATIC
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

34. Example

35. Example

36. Example

37. Example

38. Example

39. For More
Practice:
Solve for x
=

41. Solve for x:
3X + 5 = 5X – 3
30
seconds
Time is
up!!!

42. Solve for x:
2x + 7 = 9x – 4
30
seconds
Time is
up!!!

43. Solve for x:
x2
+ 7x = 9x – 1
30
seconds
Time is
up!!!

44. Solve for x:
2x2
+ 3x = x +12
60
seconds
Time is
up!!!