● 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.

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Presentation transcript:

● 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

S TEPS TO S OLVING E QUATIONS ● 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.

I NVERSE O PERATION The operation that reverses the effect of another operation. Example: Addition and subtraction are inverse operations Another Example: Multiplication and division are inverse operations.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. a.k – 18 = 13

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. a.k – 18 = 13 k = Write a related addition sentence.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. a.k – 18 = 13 k = Write a related addition sentence. k = 31

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. b.20 + x = 32

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. b.20 + x = 32 x = 32 – 20 Write a related subtraction sentence.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. b.20 + x = 32 x = 32 – 20 Write a related subtraction sentence. x = 12

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. n/6 = 18

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. c.n/6 = 18 n = 18 * 6 Write a related multiplication sentence.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. c.n/6 = 18 n = 18 * 6 Write a related multiplication sentence. n = 108

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. d.2m = 54

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. d.2m = 54 m = 54/2 Write a related division sentence.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS Example 1 Solve each equation using the inverse operations. d.2m = 54 m = 54/2 Write a related division sentence. m = 27

S OLVING E QUATIONS U SING I NVERSE O PERATIONS 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

S OLVING E QUATIONS U SING I NVERSE O PERATIONS 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

S OLVING E QUATIONS U SING I NVERSE O PERATIONS 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 n = Write a related addition sentence.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS 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 n = Write a related addition sentence. n = 47 The number is 47.

S OLVING E QUATIONS U SING I NVERSE O PERATIONS 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 n = Write a related addition sentence. n = 47 The number is 47. Check: Since 47 – 16 = 31, the solution is correct.