3.1 Addition Property of Equality (APE)

The Addition Property of Equality if a = b, then a + c = b + c We can add a positive number to both sides of the equation and it will not change the equality. We can add a negative number to both sides of the equation and it will not change the equality. (adding a negative number is the same as subtracting a positive)

To solve for “x” x – 8 = 11 x – 8 + 8 = 11 + 8 x = 19 Goal: get “x” alone on one side of the equation. How: do the opposite of whatever is keeping “x” from being all by itself. Why: by doing the opposite operation, the # on the side of the variable cancels out. Rule: whatever you do to one side of the equation you must do to the other. x – 8 + 8 = 11 + 8 x = 19

Write answer with box around it Show your work exactly like this: Write the problem: x + 7 = 2 Add same number to both sides of “=“: - 7 x = -5 Write answer with box around it

y - 8 = -3 +8 +8 y = 5

a - 5 = -2 +5 +5 a = 3

19 = k + 7 -7 -7 12 = k

.0 a + 1.5 = 3 -1.5 -1.5 a = 1.5

A number is increased by 36 is 15. Find the number. Let x = the original number. x + 36 = 15 - 36 - 36 x = -21

A number decreased by 83 is 46. Find the number. Let x = the original number. x - 83 = 46 +83 +83 x = 129

Homework: Page 116 (2-40) even How to set up Homework: 1 Homework: Page 116 (2-40) even How to set up Homework: 1.Name, Page#, Problems Assigned 2.Must write problem 3. Show work by adding/subtracting the same amount to both sides of the equal sign 4. Show solution (box, highlight, answer column)

The weekly rent on an apartment was increased by $82 The weekly rent on an apartment was increased by $82. The new rental cost is $675. What is the previous rent? Let x = the previous rent. x + 82 = 675 - 82 - 82 x = 593