1. Do Now
Simplify.
1) (-31) ) (-12)
3) 5 – ) -8 ● -9
5) -7 ● ) 54 ÷ (-9)

2. Learn to solve one-step addition and subtraction equations with integers.

3. Equations are just like a carefully balanced scale
Equations are just like a carefully balanced scale. If both expressions on each side of the equal sign match, then they are balanced.

4. If one side is heavier than the other, the scales are tipped.

5. In algebra, we solve equations for the missing variable
In algebra, we solve equations for the missing variable. The trick is to keep the scales balanced during all steps. Meaning we want both sides to be EQUAL. In order to do this, whatever you do to one side of the equation must be done to the other.

6. In order to solve for x, we must isolate (get all by its lonesome self) the variable.
In algebra we solve equations for the missing variable. The trick is to keep the scales balanced during all steps. Let's start by looking at a simple example. We know that you know that we know you know the answer (2), but for argument's sake, let's use our scales to solve this. In order to solve for x, we must isolate (get all by its lonesome self) the variable. To do this we must get rid of that pesky 4. If we subtract 4 from the left side, the scale will be unbalanced.

7. If we subtract 4 from the left side, the scale will be unbalanced.

8. To counter this, we must also subtract 4 from the other side of the equation. Now the scales are balanced once again and all is right with the universe.

9. Don't worry, we really don't expect you to draw scales each time you need to solve an equation. We are just using this to illustrate a very important point, you must keep algebraic equations balanced at all times. In order to do this, whatever you do to one side of the equation must be done to the other.

10. Solving an equation
What does it mean?
Trying to find the value of the variable that makes the equation true
How?
You want to isolate the variable by getting the variable alone on one side of the equal sign
*remember our inverse operations

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

12. 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 rid of 16 we have to use the inverse operation. What is the opposite of adding 16?
Subtracting 16

13. r + 16 = -7
Draw “the river” to separate the equation into 2 sides
Subtract 16 from both sides
Simplify
Check your answer by substituting your answer back into the problem
r = -23
= -7
-7 = -7

14. Solving One Step Equations
Draw “the river” a line through the equal sign to separate the two sides of the equation
Get rid of anything being added or subtracted to the variable by doing the inverse operation
(Goal is to have x = ______ in the end)
What you do to one side of the equal sign you must do to the other side to keep it balanced
Always check your answers by substituting into the original equation!!

15. Solve each equation. Check each answer.
Example B
Solve each equation. Check each answer.
p + 5 = –3
–5 –5
Subtract 5 from both sides.
p = –8
Check
p + 5 = –3
–8 + 5 = –3 ?
Substitute –8 for p.
– 3 = –3 ?
True. 

16. Solve each question. Check each answer.
Example B
Solve each question. Check each answer.
–6 + x = –7
x = –1
Add 6 to both sides to
isolate the variable.
Check
–6 + x = –7
–6 + (–1) = –7 ?
Substitute –1 for x.
–7 = –7 ? 
True.

17. Solve each equation. Check each answer.
Example B
Solve each equation. Check each answer.
-40 = y – 9
-31 = y
Add 9 to both sides.
Check
-40 = y - 9
–40 = ?
Substitute –31 for y.
–40 = –40 ? 
True.

18. Solve each equation. Check each answer.
Example B
Solve each equation. Check each answer.
X + (-8)= -5
X – = -5
+ 8
+ 8
y = 3
Check
-40 = y - 9
–40 = ?
Substitute –31 for y.
–40 = –40 ? 
True.

19. You Try:
Solve each equation. Check each answer.
f -5 = 22
q + 2 = –6
y – 7 = –34
20 = x - 18
m - 16 = –9
–3 + x = –9