What you should learn
To solve equations by using addition and subtraction NCTM Curriculm Standards 2, 6 - 10
To solve equations by using addition and subtraction
NCTM Curriculm Standards 2, 6 - 10
In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:
Addition Property of Equality Equivalent Equations Subtraction Property of Equality
Addition Property of Equality
Equivalent Equations
Subtraction Property of Equality
Introduction: The Chicago Bears and the Pittsburgh Steelers have each appeared on television on Monday night a total of 44 times through the 1998 - 1999 season.
If during the next five seasons, each team appears an average of two times per season, the two teqams would still have an equal number of appearances on television on Monday nights.
This example illustrates the addition property of equality.
Addition Property of Equality: For any number a, b, and c, if a = b, then a + c = b + c
Note that c can be positive, negative, or 0. In the equation below c = 5.
In the equation below, c = -5.
If the same number is added to each side of an equation, then the result is an equivalent equation. Equivalent equations are equations that have the same solution.
To solve an equation means to isolate the variable having a coefficient of 1 on one side of the equation. You can do this by using the addition property of equality.
Exercise 1: Solve 23 + t = -16
23 + t = -16 23 + t + (-23) = -16 + (-23) t + 0 = -39 t = -39 To check that -39 is the solution, substitute -39 for t in the original equation. Check: 23 + t = -16 23 + (-39) = -16 -16 = -16 The solution is -39
23 + t = -16
23 + t + (-23) = -16 + (-23)
t + 0 = -39
t = -39
To check that -39 is the solution, substitute -39 for t in the original equation. Check: 23 + t = -16 23 + (-39) = -16 -16 = -16
To check that -39 is the solution, substitute -39 for t in the original equation.
Check:
23 + t = -16 23 + (-39) = -16 -16 = -16
23 + (-39) = -16
-16 = -16
The solution is -39
You can use equations to solve many real-world problems.
In addition to the addition property of equality, there is a subtraction property of equality that may also be used to solve equations.
Subtraction Property of Equality: For any number a, b, and c, if a = b, then a - c = b - c.
Exercise 2: Solve 190 - x = 215
190 - x = 215 190 - x - 190 = 215 - 190 -x = 25 x = -25 Check: 190 - x = 215 190 - (-25) = 215 190 + 25 = 215 215 = 215 The solution is -25.
190 - x = 215
190 - x - 190 = 215 - 190
-x = 25
x = -25
Check: 190 - x = 215 190 - (-25) = 215 190 + 25 = 215 215 = 215
190 - (-25) = 215
190 + 25 = 215
215 = 215
The solution is -25.
Most equations can be solved in two ways. Remember that subtracting a number is the same as adding its inverse.
Exercise 3: Solve a + 3 = -9
Sometimes equations can be solved more easily if they are first rewritten in a different form.
Exercise 4: Solve y - (-3/7) = -4/7
Further Application: Exploration Calculators
You can use a scientific or graphing calculatro to solve equations that involve decimals. If you're using a scientific calculator like the TI-34, you can use the plus/minus key to input negative numbers or to change the sign of any number If you're using a graphing calculator like the TI-82 or TI-83, you can use the negative key to input negative numbers On all calculators, use the subtraction key to subtract two numbers Your Turn a. Take some time to work through the examples in this lesson using your calculator. b. Describe the difference between the key you use to indicate a negative number on your calculator and the subtraction key. c. Does the order in which you use these keys matter? Why or why not? d. How would you use your calculator to solve x + (-9.016) = 5.14?
You can use a scientific or graphing calculatro to solve equations that involve decimals.
If you're using a scientific calculator like the TI-34, you can use the plus/minus key to input negative numbers or to change the sign of any number If you're using a graphing calculator like the TI-82 or TI-83, you can use the negative key to input negative numbers On all calculators, use the subtraction key to subtract two numbers
If you're using a scientific calculator like the TI-34, you can use the plus/minus key to input negative numbers or to change the sign of any number
If you're using a graphing calculator like the TI-82 or TI-83, you can use the negative key to input negative numbers
On all calculators, use the subtraction key to subtract two numbers
Your Turn
a. Take some time to work through the examples in this lesson using your calculator. b. Describe the difference between the key you use to indicate a negative number on your calculator and the subtraction key. c. Does the order in which you use these keys matter? Why or why not? d. How would you use your calculator to solve x + (-9.016) = 5.14?
a. Take some time to work through the examples in this lesson using your calculator.
b. Describe the difference between the key you use to indicate a negative number on your calculator and the subtraction key.
c. Does the order in which you use these keys matter? Why or why not?
d. How would you use your calculator to solve x + (-9.016) = 5.14?
Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.
Homework: The homework to be assigned for tonight would be: 15 - 37 odd, 38, 39, 41 - 47
Alternative Homework: Enriched: 14 - 36 even, 38 - 47
Extra Practice: Students book page 762 Lesson 3-1
Extra Practice Worksheet: Click Here.
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