● a variable is a letter which represents an unknown number. any letter can be used as a variable....
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EQUATIONS
●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
●An equation is a sentence that states that two mathematical expressions are equal.
●Example: 2x-16=18
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.
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.
SOLVING EQUATIONS USING INVERSE OPERATIONS
Example 1Solve each equation using the inverse
operations.a. k – 18 = 13
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.
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
SOLVING EQUATIONS USING INVERSE OPERATIONS
Example 1Solve each equation using the inverse
operations.b. 20 + x = 32
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.
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
SOLVING EQUATIONS USING INVERSE OPERATIONS
Example 1Solve each equation using the inverse
operations.• n/6 = 18
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.
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
SOLVING EQUATIONS USING INVERSE OPERATIONS
Example 1Solve each equation using the inverse
operations.d. 2m = 54
SOLVING EQUATIONS USING INVERSE OPERATIONS
Example 1Solve each equation using the inverse
operations.d. 2m = 54
m = 54/2 Write a related division sentence.
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
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
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
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.
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.
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.