Upload
anissa-wells
View
222
Download
1
Embed Size (px)
Citation preview
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
AF4.0 Students solve simple linear equations and inequalities over the rational numbers.
California Standards
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
m + 4.6 = 9m + 4.6 = 9
Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition.
Once you have solved an equation, it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation.
Remember!
Additional Examples 1A: Solving Equations with Decimals
Solve.
4.4 m =– 4.6 – 4.6
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
8.2p = –32.8
–4p =
Since p is multiplied by 8.2, divide both sides by 8.2.
–32.8 8.2
8.2p 8.2
=
Additional Examples 1B: Solving Equations with Decimals
Solve.
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Additional Examples 1C: Solving Equations with Decimals
x = 18
Since x is divided by 1.2, multiply both sides by 1.2.
= 15x 1.2
x 1.2
= 1.2 • 15 1.2 •
Solve.
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
m + 9.1 = 3
m + 9.1 = 3Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition.
Check It Out! Example 1
–6.1 m =
–9.1 = –9.1
Solve.A.
B. 5.5b = 75.9
75.9 5.5
5.5 5.5 =b
13.8b =
Since b is multiplied by 5.5, divide both sides by 5.5.
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
= 90
Check It Out! Example 1C
y = 405
Since y is divided by 4.5, multiply both sides by 4.5.
y 4.5
y 4.5
= 4.5 • 904.5 •
Solve.
C.
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Additional Example 2A: Solving Equations with Fractions
= – 3 7
n + 2 7
n + – = – –3 7
2 7
27
27
n = – 5 7
Solve.
2 7Since is added to n, subtract
from both sides.
2 7
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
1 6 = 2
3y –
Additional Example 2B: Solving Equations with Fractions
Find a common denominator, 6.=y 4 6
1 6
+
=y – 2 3
1 6
Solve.
Since is subtracted from y, add
to both sides.
1 61
6
+1 6
+ 1 6
=y 5 6
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
5 6 =
5 8x
6 5••
6 5
5 6
= 5 8
x
Multiply by the reciprocal.
Simplify.
Additional Example 2C: Solving Equations with Fractions
x =3 4
3
4
Solve.
Since x is multiplied by ,
divide both sides by .5 6
5 65
6÷ = ÷5
8x 5
65 6
1
11
1
1
1
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
1 9
= – 5 9
n +
Check It Out! Example 2A
n = – 2 3
Simplify.
Solve.
n + – = – –5 9
1 9
19
19
n = – 6 9
1 9Since is added to n, subtract
from both sides.
1 9
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 2B
y = 1 1 4
Solve.
Simplify.
=y – 1 2
3 4
Find a common denominator, 4.=y 3 4
2 4
+
=y – 3 4
1 2
Since is subtracted from y, add
to both sides.
1 21
2
+1 2
+ 1 2
=y 5 4
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 2C
Solve.
3 8 =
3 4x
8 3••
8 3
3 8
= 3 4
x
Multiply by the reciprocal.
Simplify.
x = 2
2
1
Since x is multiplied by ,
divide both sides by .3 8
3 83
8÷ = ÷3
4x 3
83 8
1
1
1
11
1
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Write an equation:
Amount Needed 1/3Amount Saved
Additional Example 3: Solving Word Problems Using Equations
=
Janice has saved $21.40. This is of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save?
1 3
a1 3 = $21.40
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Additional Example 3 Continued
Janice needs to save $64.20.
1 3 = 21.40 a 3
13 1
a = 64.20
Multiply by the reciprocal.
Simplify.
Since a is multiplied by ,
divide both sides by .1 3
1 3= 21.40 ÷a x ÷1
31 3
1 3
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Write an equation:
Capacity of minivan’s tank
2/3 Capacity of car’s tank• =
Check It Out! Example 3
g 242 3
Rick’s car holds the amount of gasoline as his
wife’s van. If the car’s gas tank can hold 24
gallons of gasoline, how much gasoline can the tank in the minivan hold?
2 3
• =
Evaluating Algebraic Expressions
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 3 Continued
The minivan can hold 36 gallons of gas.
2 3 = 24 g 3
23 2
g = 36
Multiply by the reciprocal.
Simplify.
Since g is multiplied by ,
divide both sides by .2 3
2 3= 24 ÷g ÷2
32 3
2 3
g = 722