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EQUATIONS

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Page 1: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

EQUATIONS

Page 2: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

●A variable is a letter which represents an unknown number. Any letter can be used as a variable.

●An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z

●A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number and 3”

represents “n+3.”

Review of Terms

Page 3: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

●An equation is a sentence that states that two mathematical expressions are equal.

●Example: 2x-16=18

Page 4: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

STEPS TO SOLVING EQUATIONS

●Simplify each side of the equation, if needed, by distributing or combining like terms.

●Move variables to one side of the equation by using the opposite/inverse operation of addition or subtraction.

●Isolate the variable by applying the opposite operation to each side.• First, use the opposite operation of

addition or subtraction. • Second, use the opposite operation of

multiplication or division.●Check your answer.

Page 5: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

INVERSE OPERATION

The operation that reverses the effect of another operation.

Example: Addition and subtraction are inverse operations

Another Example: Multiplication and division are inverse operations.

Page 6: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.a. k – 18 = 13

Page 7: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.a. k – 18 = 13

k = 13 + 18 Write a related addition sentence.

Page 8: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.a. k – 18 = 13

k = 13 + 18 Write a related addition sentence.

k = 31

Page 9: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.b. 20 + x = 32

Page 10: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.b. 20 + x = 32

x = 32 – 20 Write a related subtraction sentence.

Page 11: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.b. 20 + x = 32

x = 32 – 20 Write a related subtraction sentence.

x = 12

Page 12: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.• n/6 = 18

Page 13: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.c. n/6 = 18

n = 18 * 6 Write a related multiplication sentence.

Page 14: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.c. n/6 = 18

n = 18 * 6 Write a related multiplication sentence.

n = 108

Page 15: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.d. 2m = 54

Page 16: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.d. 2m = 54

m = 54/2 Write a related division sentence.

Page 17: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 1Solve each equation using the inverse

operations.d. 2m = 54

m = 54/2 Write a related division sentence.

m = 27

Page 18: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 2• A number decreased by sixteen is 31.

Find the number.• Let n represent the number. Translate

the words into an equation using the variable.

• A number decreased by 16 is 31

Page 19: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 2• A number decreased by sixteen is 31.

Find the number.• Let n represent the number. Translate

the words into an equation using the variable.

• A number decreased by 16 is 31 n – 16 = 31

Page 20: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 2• A number decreased by sixteen is 31. Find

the number.• Let n represent the number. Translate the

words into an equation using the variable.• A number decreased by 16 is 31n – 16 = 31n = 31 + 16 Write a related addition

sentence.

Page 21: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 2• A number decreased by sixteen is 31.

Find the number.• Let n represent the number. Translate

the words into an equation using the variable.

• A number decreased by 16 is 31n – 16 = 31n = 31 + 16 Write a related addition

sentence.n = 47 The number is 47.

Page 22: ● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable

SOLVING EQUATIONS USING INVERSE OPERATIONS

Example 2• A number decreased by sixteen is 31. Find

the number.• Let n represent the number. Translate the

words into an equation using the variable.• A number decreased by 16 is 31n – 16 = 31n = 31 + 16 Write a related addition

sentence.n = 47 The number is 47.

Check: Since 47 – 16 = 31, the solution is correct.