Solving One and Two step Equations

Sol A.1

Why do we do the same thing to both sides of an equation

d + 12 = -5

Why do we do the same thing to both sides of an equation

• https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--simple-equations

Ex. 1) Solve r + 16 = -7Think of this equation as a balance scale.

Whatever you do to one side has to be done to the other to keep it balanced!

1) Solve r + 16 = -7

- 16 -16 r = -23

-23 + 16 = -7

1) Solve r + 16 = -71. Draw “the river” to

separate the equation into 2 sides

2. Subtract 16 from both sides

3. Simplify vertically4. Check your answer by

substituting your answer back into the problem

Ex. 2) Solve x + 2 = -3

2) Solve x + 2 = -31. Draw “the river” to

separate the equation into 2 sides

2. Subtract 2 from both sides

3. Simplify vertically4. Check your answer by

substituting your answer back into the problem

- 2 - 2 x = -5

-5 + 2 = -3

On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

Addition and subtraction Properties of Equality

• Definition: Either adding or subtracting the same number to each side of the equation produces an equivalent equation.

Example:X - 9 = 15

How can you check your answers?

Try These: Don’t forget to check your answer

3. r – 2 = 21

4. m + 17 = 3

5. b – (-4) = 9

3. r – 2 = 21

4. m + 17 = 3

5. b – (-4) = 9

Multiplication and Division Properties of Equality

Definition: If you multiply or divide each side of the equation by the same nonzero number you produce an equivalent equation.

Example 6:Multiplication:

416

p

Division:Example 7. 7m=91

Try These:8. -6m = 489. 14 = -x10.

73

x

8. -6m = 48

9. 14 = -x

10.

73

x

Solving Equations using Reciprocals

Rule – When the original number is multiplied by it’s reciprocal the product should equal 1.

Example 11:Don’t forget to check your answer

4

7

2

x

Example 12

95

3x

Solving Two Step Equations

Note- When solving two step equations Always Isolate the variable first. (i.e. get rid of anything that is not with your variable.)

Example 13: 115

2

x

Solving Two Step Equations

Example 14: 2495 x

Try These:

15.

16.

17.

1644 y

234

x

73

1 z

15. 1644 y

16.

234

x

17. 73

1 z

Solving Two-Step equations by combining like terms

Example:18. 7x – 4x = 21 19. 5b – 7b = 4