Lesson 3.1 – Solve One Step Equations Vocabulary 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)
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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)
Lesson 3.1 – Solve One Step EquationsVocabulary
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!
Solve each equation. CHECK your solution.
2) b - 17 = 12
+17 +17
b = 29
Check:
b - 17 = 12
29 - 17 = 12
12 = 12
You Try It!
Solve each equation. CHECK your solution.
3) -3 = x + 2
-2 -2
-5 = x
x = -5
Check:
-3 = x + 2
-3 = -5 + 2
-3 = -3
You Try It!
Solve each equation. CHECK your solution.
4) y - 4 = -6
+4 +4
y = -2
Check:
y - 4 = -6
-2 - 4 = -6
-6 = -6
Lesson 3.1 – Solve One Step EquationsVocabulary
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!
Solve each equation. CHECK your solution.
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