Download Chapter 1.2-1.3 Solving Equations by Adding, Subtracting

Chapter 1.2­1.3 Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
August 18, 2016
Bellwork:
Homework Questions???
Write as a fraction and reduce if you can: 1) 2.7
2) 0.325
Write each as a decimal, use repeating decimals when necessary:
3) 5/2
4) 6/8
Evaluate:
5) 2x + y; x = 4, y = 5 Aug 11­10:09 AM
Aug 11­10:15 AM
Vocabulary:
Chapter 1.2 Solving Equations by Adding of Subtracting
Solve one­step equations in one variable by using addition or subtraction.
Equations: mathematical statement that two expressions are equal
Solution of an Equation: a value of the variable that makes the equation true.
Aug 11­10:15 AM
Think of Equations like scales, that show two quantities are equal.
Aug 11­10:16 AM
We solve equations by using inverse (opposite) operations. Inverse operations "undo" operations on the variable. What are the inverse operations of the following: Addition
Multiplication
Subtraction
Division
x + 5 = 10 Aug 11­10:18 AM
Aug 12­8:06 AM
1
Chapter 1.2­1.3 Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
August 18, 2016
Solve each equation by using addition: Solve Each Equation. Check your answer.
Remember to keep the equation balanced by performing the same operation to both sides.
x ­ 9 = 12
Example 1: ¾ = t ­ ¼
Add x
x ­ 9 = 12
+9 +9
x = 21
Subtract x
Check your solution, by substituting the value for the variable: You Try 1: n ­ 3.2 = 5.6
x ­ 9 = 12
(21) ­ 9 = 12
12 = 12 Aug 11­10:20 AM
Aug 11­3:12 PM
Solve Each Equation. Check your answer.
Solving Equations by Using Subtraction:
At times you will need to subtract to isolate the variable.
Example 2:
0.8 = m + 6.3
x + 8 = 14
Add x
x + 8 = 14
­ 8 ­8
x = 6
Subtract x
You Try 2: d + 1/3 = 1
Check your answer:
x + 8 = 14
(6) + 8 = 14
14 = 14
Aug 11­3:17 PM
Remember; subtracting it the same as adding the opposite. At times it may be easier to add the opposite to both sides instead of subtracting.
­6 + a = 3
Aug 11­3:27 PM
Solve each equation. Check your answer.
Example 3: ­2.3 + m = 7
The opposite of ­6 is 6.
­6 + a = 3
+6 +6
You Try 5:
­3/4 + z = 5/4
a = 9
Check ­6 + a = 3
­6 + (9) = 3
3 = 3
Aug 11­3:29 PM
Aug 11­3:44 PM
2
Chapter 1.2­1.3 Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
August 18, 2016
Application:
Properties of Equality words
numbers You can add the same 3 = 3
Addition Property number to both sides of an 3 + 2 = 3 + 2
of Equality
equation, and the statement 5 = 5
will still be true.
Subtraction Property of Equality
You can subtract the same number from both sides of an equation, and the statement will still be true.
algebra
a = b
a + c = b + c
7 = 7
7 ­ 5 = 7 ­ 5
2 = 2
A person's maximum heart rate is the highest rate, in beats per minute, that person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15­year­old.
a = b
a ­ c = b ­ c
Aug 11­3:47 PM
Aug 11­3:53 PM
Solving Equations by Using Multiplication:
Chapter 1.3 Solving Equations by Multiplying of Dividing
Keep the equation balanced while using inverse operations.
Solve one­step equations in one variable by using multiplication of division.
Check answer
Aug 12­7:58 AM
Solve each equation. Check your answer.
Example 1:
Aug 12­7:58 AM
Solving Equations by using Division:
Keep the equation balanced.
8x = 72
You Try 1:
8x = 72
8 8
Check answer
8x = 72
8(9) = 72
72 = 72
x = 9
Aug 12­7:59 AM
Aug 12­7:59 AM
3
Chapter 1.2­1.3 Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
August 18, 2016
Solving Equations that contain Fractions:
Solve each equation. Check your answers.
Example 2:
15 = ­4z
Remember that dividing is the same as multiplying by the reciprocal.
4 ÷ 2 = 4(½)
2 = 2
When solving equations with fractions is may be easier to multiply by the reciprocal instead of dividing.
You Try 3: 0.5x = ­10
Check Answer
Aug 12­8:00 AM
Solve each Equation. Check you answers.
Aug 12­8:01 AM
Properties of Equality
words
Example 3:
numbers
You can multiply both 6 = 6
Multiplication sides of an equation by the 6(3) = 6(3)
Property of Equality same number, and the 18 =18
statement will still be true
You Try 5: algebra
a = b
ac = bc
You can divide both sides 8 = 8
a = b
Division Property of of an equation by the same 8 ÷ 4 = 8 ÷ 4 a ÷ c = b ÷ c
Equality
nonzero number, and the 2 = 2
(c ≠ 0)
statement will still be true.
Aug 12­8:01 AM
Aug 12­8:02 AM
Application:
The distance in miles from the airport that a plane should begin descending, divided by 3 equals the plane's height above the ground in thousands of feet. If a plane is 10,000 feet above ground, write and solve an equation to find the distance at which the pilot should begin descending.
Homework:
P. 20­22 # 21­57, and
P. 27­28 #19­47
(all odds)
A plane began descending 45 miles from the airport. Use the equation above to find how high the plane was flying when the descent began.
Aug 12­8:02 AM
Aug 11­3:56 PM
4
Chapter 1.2­1.3 Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook
August 18, 2016
Aug 12­7:32 AM
5