3.1 Solving Equations Using Addition and Subtraction - PowerPoint PPT Presentation


Title: 3.1 Solving Equations Using Addition and Subtraction


1
Two operations that undo each other, such as
addition and subtraction, are called inverse
operations. Inverse operations help you to
isolate the variable on one side of the equal
sign.
The problem.
Use inverse property.
Simplify.
Check
?
?
?
?
Formally check even numbered homework problems.
2
2-3 Solving Equations Using Multiplication and
Division
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
3
What equation is shown on the scale?
1
To isolate the variable, divide by 2, but to keep
the equation in balance whatever you do to one
side you must do to the other side.
The value or values of the variable that make the
statement true is the solution to the equation.
4
Write an equation for the following
There is only part of a variable. To get a whole
variable use repeated addition which is known as
multiplication.
1
The value or values of the variable that make the
statement true is the solution to the equation.
5
Multiplication and division are inverse
operations. You can use multiplication to undo
division, and division to undo multiplication.
Write the problem.
1
Use inverse property.
1
Simplify.
Check
Check
The 4 must be in the numerator position or
midway. It should not be written in the
denominator position!
?
?
?
6
Solve.
Example 1
Example 2
Example 3
1
1
2
1
Do your arithmetic calculations off to the side
(margins).
The 7 must be in the numerator position or
midway. It should not be written in the
denominator position!
Leave the fraction improper in lowest terms.
Use good form - place the negative sign out front
in your answer.
7
Write an equation and then solve.
Ex.4 15 is the quotient of a number and negative
8.

Do NOT switch the variable to the other side of
the equal sign unless you have reason to move it!
1
8
CHANGING DECIMALS TO INTEGERS
You can multiply an equation with decimal
coefficients by a power of ten to get an
equivalent equation with integer coefficients.
Multiply each side of the equation by a power of
10 to rewrite the equation without decimals.
Use the LCM (least common multiple) to determine
the power of ten needed to clear the decimal/s.
Recall that multiplying a number by 10, 100, or
1000 is equivalent to moving the decimal point
to the right one, two, or three place
respectively.
0.25 10 2.5
0.25 100 25
0.25 1000 250
9
Solve.
Write the problem.
Multiply by LCM.
Distribute.
Use inverse operations.
10
Solve.
Write the problem.
Multiply by LCM.
Distribute.
Use inverse operations.
Show division work neatly beside the equation.
Remember In algebra work downward. Line up the
equal signs. Skip one line after the answer.
11
Example 5 Solve. Round to the nearest tenth.
Example 6 Solve. Round to the nearest hundredth.
Example 7 Solve. Round to the nearest tenth if
necessary.
You need to divide to what decimal position in
order to round to hundredths?
You need to divide to what decimal position in
order to round to tenths?
12
Example 5 Solve. Round to the nearest tenth.
Example 6 Solve. Round to the nearest hundredth.
13
Example 7 Solve. Round to the nearest tenth if
necessary.
14
Homework
2-A5 Pages 88-89 14-25,28,46,55,57.
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3.1 Solving Equations Using Addition and Subtraction

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Title: 3.1 Solving Equations Using Addition and Subtraction


1
Two operations that undo each other, such as
addition and subtraction, are called inverse
operations. Inverse operations help you to
isolate the variable on one side of the equal
sign.
The problem.
Use inverse property.
Simplify.
Check
?
?
?
?
Formally check even numbered homework problems.
2
2-3 Solving Equations Using Multiplication and
Division
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
3
What equation is shown on the scale?
1
To isolate the variable, divide by 2, but to keep
the equation in balance whatever you do to one
side you must do to the other side.
The value or values of the variable that make the
statement true is the solution to the equation.
4
Write an equation for the following
There is only part of a variable. To get a whole
variable use repeated addition which is known as
multiplication.
1
The value or values of the variable that make the
statement true is the solution to the equation.
5
Multiplication and division are inverse
operations. You can use multiplication to undo
division, and division to undo multiplication.
Write the problem.
1
Use inverse property.
1
Simplify.
Check
Check
The 4 must be in the numerator position or
midway. It should not be written in the
denominator position!
?
?
?
6
Solve.
Example 1
Example 2
Example 3
1
1
2
1
Do your arithmetic calculations off to the side
(margins).
The 7 must be in the numerator position or
midway. It should not be written in the
denominator position!
Leave the fraction improper in lowest terms.
Use good form - place the negative sign out front
in your answer.
7
Write an equation and then solve.
Ex.4 15 is the quotient of a number and negative
8.

Do NOT switch the variable to the other side of
the equal sign unless you have reason to move it!
1
8
CHANGING DECIMALS TO INTEGERS
You can multiply an equation with decimal
coefficients by a power of ten to get an
equivalent equation with integer coefficients.
Multiply each side of the equation by a power of
10 to rewrite the equation without decimals.
Use the LCM (least common multiple) to determine
the power of ten needed to clear the decimal/s.
Recall that multiplying a number by 10, 100, or
1000 is equivalent to moving the decimal point
to the right one, two, or three place
respectively.
0.25 10 2.5
0.25 100 25
0.25 1000 250
9
Solve.
Write the problem.
Multiply by LCM.
Distribute.
Use inverse operations.
10
Solve.
Write the problem.
Multiply by LCM.
Distribute.
Use inverse operations.
Show division work neatly beside the equation.
Remember In algebra work downward. Line up the
equal signs. Skip one line after the answer.
11
Example 5 Solve. Round to the nearest tenth.
Example 6 Solve. Round to the nearest hundredth.
Example 7 Solve. Round to the nearest tenth if
necessary.
You need to divide to what decimal position in
order to round to hundredths?
You need to divide to what decimal position in
order to round to tenths?
12
Example 5 Solve. Round to the nearest tenth.
Example 6 Solve. Round to the nearest hundredth.
13
Example 7 Solve. Round to the nearest tenth if
necessary.
14
Homework
2-A5 Pages 88-89 14-25,28,46,55,57.
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