2-4 Solving Multi-Step Equations and Consecutive Integer Problems Algebra 1 Glencoe McGraw-Hill Linda Stamper

Solving Multi-Step Equations The prefix “multi” means “more than one”. A multi-step equation is solved by transforming the equation more than one time. Always remember the basic rule: Whatever you do to one side of the equal sign, you must also do to the other side of the equal sign. When solving multi-step equations, undo the addition or subtraction first before undoing multiplication or division.

Undo fraction using the reciprocal. Solve. Write the problem. Undo subtraction. 1 Undo fraction using the reciprocal. Remember: In algebra work downward. Line up the equal signs. Skip one line after the answer.

Solve. Write the problem. Undo addition. 1 Undo division. The 5 must be in the numerator position or midway. It should not be written in the denominator position!

Solve. Write the problem. Change subtraction to addition and distribute. +– – Combine like terms. Undo double sign. Undo subtraction. 1 Undo multiplication.

Are your equal signs in a line? Solve. Example 2 Example 3 Example 1 +– – +– – Combine like terms. Distribute Are your equal signs in a line?

Solve. Example 4 Example 5 Example 6 1 1 4 1 2 Multiply both sides by the reciprocal.

The study of numbers and the relationship between them is called number theory. Consecutive integers are integers in counting order, such as 7, 8, and 9. Beginning with an odd integer and counting by two will result in consecutive odd integers, such as -3, -1, 1, 3, 5 Beginning with an even integer and counting by two will result in consecutive even integers, such as -4, -2, 0, 2, 4

Two consecutive integers have a sum of 77. Find the integers. Assign Labels. Let f = first integer Let f + 1 = second integer Verbal Model. first integer + second integer = total f + ( f + 1) = 77 Algebraic Model. Solve. The integers are 38 and 39. Sentence. Check  38 + 39 = 77

Two consecutive odd integers have a sum of 92. Find the integers. Assign Labels. Let f = first integer Let f + 2 = second integer Verbal Model. first integer + second integer = total f + ( f + 2) = 92 Algebraic Model. Solve. The integers are 45 and 47. Sentence. Check  45 + 47 = 92

Example 7 Find three consecutive integers whose sum is 195. Example 8 Find two consecutive odd integers whose sum is –96. Example 9 Find three consecutive even integers whose sum is -42. Assign Labels. Verbal Model. Algebraic Model. Solve. Sentence.

Example 7 Find three consecutive integers whose sum is 195. Assign Labels. Let f = first integer Let f + 1 = second integer Let f + 2 = third integer Verbal Model. first # + second # + third # = total f + ( f +1) + ( f + 2) = 195 Algebraic Model. Solve. The integers are 64, 65 and 66. Sentence.  Check 64 + 65 + 66 = 195

Example 8 Find two consecutive odd integers whose sum is –96. Assign Labels. Let f = first integer Let f + 2 = second integer Verbal Model. first integer + second integer = total f + ( f +2) = -96 Algebraic Model. Solve. The integers are -49 and -47. Sentence.  Check -49 + -47 = -96

Example 9 Find three consecutive even integers whose sum is -42. Assign Labels. Let f = first number Let f + 2 = second number Let f + 4 = third number Verbal Model. first # + second # + third # = total f + ( f +2) + ( f + 4) = -42 Algebraic Model. Solve. The integers are -16, -14 and -12. Sentence.  Check -16 + (-14) + (-12) = -42

Homework 2-A6 Pages 95-97 #11-26,32-38,47.