Warm Up You need your calculator and acti-vote 1.-3(4x – 8) +7(-4 + 3x) 2.-4(2n + 3) – 2(1 + 2n)

HW Solutions 2.21x m x m x m x m x m x m x m x m m + 18

Objective The student will be able to: solve equations using addition and subtraction. solve equations using multiplication and division.

1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

r = = -7 1) Solve r + 16 = -7 1.Draw “the river” to separate the equation into 2 sides 2.Subtract 16 from both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem

2) Solve x + 2 = -3 Get the variable by itself. What is your first step? 1.Add 2 to both sides 2.Subtract 2 from both sides 3.Add 3 to both sides 4.Subtract 3 from both sides Answer Now

2) Solve x + 2 = x = = -3 1.Draw “the river” to separate the equation into 2 sides 2.Subtract 2 from both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

3) Solve 8 = m m = 5 2.m = 11 3.m = 24 4.m = 8/3 Answer Now

3) Solve 8 = m = m 8 = Draw “the river” to separate the equation into 2 sides 2.Add 3 to both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem

When solving equations, we want to eliminate double signs. y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

4) Solve y + (-3) = 7 y – 3 = y = (-3) = 7 1.Draw “the river” to separate the equation into 2 sides 2.Eliminate the double sign 3.Add 3 to both sides 4.Simplify vertically 5.Check your answer by substituting your answer back into the problem

5) Solve. -x - (-2) = 1 -x + 2 = x = -1 x = 1 -(1) + 2 = 1 1.Draw “the river” to separate the equation into 2 sides 2.Eliminate the double sign 3.Subtract 2 from both sides 4.Simplify vertically 5.We haven’t gotten x by itself. If we read this aloud, it is “the opposite of x equals -1”. What would x be equal? 6.Check your answer

Solve -y – (-3) = 7 1.y = 10 2.y = 4 3.y = y = -4 Answer Now

6) Solve. -5t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation will we use? division

6) Solve -5t = t = (-12) = 60 1.Draw “the river” to separate the equation into 2 sides 2.Divide both sides by -5 3.Simplify 4.Check your answer

7) Solve 15 = 6n = n 15 = 6(2.5) 1.Draw “the river” 2.Divide both sides by 6 3.Simplify 4.Check your answer

8) Solve -3v = v = v = v = 43 4.v = 126 Answer Now

9) Solve You don’t like fractions? Let’s get rid of them! “Clear the fraction” by multiplying both sides of the equation by the denominator.

9) Solve 4 · · 4 x = Draw “the river” 2.Clear the fraction – multiply both sides by 4 3.Simplify 4.Check your answer

3 · = 18 · 3 2x = x = 27 1.Draw “the river” 2.Clear the fraction – multiply both sides by 3 3.Simplify 4.Divide both sides by 2 5.Simplify 6.Check your answer 10) Solve = 18

11) Which step clears the fraction in 1.Multiply by 3 2.Multiply by 5 3.Multiply by Multiply by -5 Answer Now

12) Solve 1.b = b = b = 14 4.b = 56 Answer Now

Example 13 Katie is twice as old as her sister Mara. The sum of their ages is 24. How old is each sister?

Example 14 Twenty-one subtracted from a number is -8. Find the number