inverse operations operations which reverse the effect of

Lesson 3.1 – Solve One Step EquationsVocabulary

Inverse Operations – Operations which reverse the effect

of each other.

Addition Subtraction

Multiplication Division

Squaring a number Taking the square root of a number

Equivalent expressions– Expressions which have the same

solution(s)


Addition Property of Equality

Adding the same number to each side of an equation

produces an equivalent equation.

If x - a = b, then x - a + a = b + a or x = b + a .

Subtraction Property of Equality

Subtracting the same number from each side of an

equation produces an equivalent equation.

If x + a = b, then x + a - a = b - a or x = b - a .

Solve an equation using subtractionEXAMPLE 1

Solve y + 3 = 10.

Write original equationy + 3 = 10

– 3 – 3Use subtraction property of equality:

Subtract 3 from each side.

y = 7

ANSWER

The solution is y = 7.

Solve an equation using subtractionEXAMPLE 1

CHECK Substitute 7 for y in the original equation.

y + 3 = 10 Write original equation.

7 + 3 = 10?

Substitute 7 for y.

10 =10 Simplify. Solution checks.

Solve an equation using additionEXAMPLE 2

Solve 11 = t – 9

Write original equation.11 = t – 9

Add 9 to each side.+9 +9

20 = t Simplify.

Write the solution with the variable on the left: t = 20

Solve an equation using additionEXAMPLE 2

Check:

Write original equation. 11 = t – 9

Substitute solution for t.

Check.

11 = 20 - 9

11 = 11

You Try It!

Solve each equation. CHECK your solution.

1) a + 6 = 17

-6 -6

a = 11

Check:

a + 6 = 17

11 + 6 = 17

17 = 17

You Try It!


2) b - 17 = 12

+17 +17

b = 29

Check:

b - 17 = 12

29 - 17 = 12

12 = 12

You Try It!


3) -3 = x + 2

-2 -2

-5 = x

x = -5

Check:

-3 = x + 2

-3 = -5 + 2

-3 = -3

You Try It!


4) y - 4 = -6

+4 +4

y = -2

Check:

y - 4 = -6

-2 - 4 = -6

-6 = -6


Multiplications Property of Equality

Multiplying each side of an equation by the same non-

zero number produces an equivalent equation.

If x = b and a ≠ 0, then a • x = ab or x = ab.

a a

Division Property of Equality

Dividing each side of an equation by the same non-

zero number produces an equivalent equation.

If ax = b and a ≠ 0, then ax = b or x = b.

a a a

Solve an equation using divisionEXAMPLE 3

Solve 8x = 56.

8x = 56

x = 7

Write original equation.

8x

8

56

8= Divide each side by 8.

Simplify.

The solution is x = 7

The division property of equality can be used to solve

equations involving multiplication.

Solve an equation using divisionEXAMPLE 3

Check:

Write original equation. 8x = 56

Substitute solution for x.

Check.

8(7) = 56

56 = 56

Solve an equation using multiplicationEXAMPLE 4

Write original equation.

5a5

= 5 12Multiply each side by 5.

a = 60 Simplify.

= 12a5

Solve

SOLUTION

= 12a5

5a5

= 5 12 Fives cancel.

Solve an equation using multiplicationEXAMPLE 4

Check:

Write original equation.= 12

Substitute solution for x.

Check.

= 12

12 = 12

5

a

60

5

Solve an equation by multiplying by a reciprocalEXAMPLE 5

SOLUTION

Write original equation.t = 63

5

t = 63

5Solve

53

The coefficient of t is

3

5The reciprocal of

5

3is

( )(t ) =3

5

5

3

5

36 Multiply each side by the

5

3reciprocal,

Solve an equation by multiplying by a reciprocalEXAMPLE 5

t = 10Simplify.

ANSWER

The solution is t =10. Check by substituting 10 for t in

the original equation.

CHECK Write original equation.

Substitute 10 for t.

6 = 6 Simplify. Solution checks.

t = 63

5

(10) = 6?3

5

( )(t ) =5 3

3 5

5

36

2

You Try It!


5) 3x = 39

3 3

Check:

3x = 39

3(13)=39

39= 39

x = 13

You Try It!

Solve each equation. CHECK your solution.6) b = 13

4

Check:

b = 13

4

52 = 13

4

13= 13

4 • b = 4 • 13

4

b = 52

You Try It!


7) . -24 = 4x

4 4

Check:

-24 = 4x

-24 = 4(-6)

-24 = -24

-6 = x

x = -6

You Try It!


8) -m = 21

-1 -1

Check:

-(-21) = 21

-21 = 21

m = -21

You Try It!


x = 602

3

( x ) =2

3

3

2

3

260

x = 90

CHECK

inverse operations operations which reverse the effect of

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