1. Bell Ringer What value(s) of x make the sentence true? 7 + x = 12
x = x2
x = 1 x
5. x + 5 = x + 2

2. To Solve an Equation in one variable means...
To isolate the variable having a coefficient of 1 on one side of the equation.
Ex: x = 5 is solved for x.

3. Addition Property of Equality
For any numbers a, b, and c, if a = b, then a + c = b + c.
What it means:
You can add any number to BOTH sides of an equation and the equation will still hold true.

4. Let’s try an example! Always check your solution!!
The original problem is x - 6 = 10.
Using the solution x=16,
Does = 10?
YES! 10 = 10 and our solution is correct.
x - 6 = 10 Add 6 to each side x = 16

5. What if we see y + (-4) = 9? Check your solution!
Does = 9?
YES! 9=9 and our solution is correct.
Recall that y + (-4) = 9 is the same as y - 4 = 9. Now we can use the addition property. y - 4 = y = 13

6. How about z = 7?
Remember to always use the sign in front of the number.
Because 16 is negative, we need to add 16 to both sides.
-16 + z = 7
z = 23
Check you solution!
Does = 7?
YES! 7 = 7 and our solution is correct.

7. What it means: Subtraction Property of Equality
For any numbers a, b, and c, if a = b, then a - c = b - c.
What it means:
You can subtract any number from BOTH sides of an equation and the equation will still hold true.

8. 3 Examples: 3) z - (-5) = -13 Change this equation. z + 5 = -13 -5 -5
x = 14
Does = 17?
2) 13 + y = 20
y = 7
Does = 20?
3) z - (-5) = -13
Change this equation. z + 5 = -13
z = -18
Does -18 -(-5) = -13?
= -13
-13 = -13 YES!

9. Multiplication Property of Equality
For any numbers a, b, and c, if a = b,
then ac = bc.
What it means:
You can multiply BOTH sides of an equation by any number and the equation will still hold true.

10. Let’s try an example! Always check your solution!!
The original problem is
x = 18 2
Using the solution x = 36,
Is 36/2 = 18?
YES! 18 = 18 and our solution is correct.
x = 18 2 Multiply each side by 2. (2)x = 18(2) x = 36

11. What do we do with negative fractions?
The two negatives will cancel each other out.
The two fives will cancel each other out.
(-5) (-5)
x = -15
Does -(-15)/5 = 3?
Recall that
Solve
Multiply both sides by -5.

12. Division Property of Equality
For any numbers a, b, and c (c ≠ 0), if a = b, then a/c = b/c
What it means:
You can divide BOTH sides of an equation by any number - except zero- and the equation will still hold true.
Why did we add c ≠ 0?

13. 2 Examples: 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6
x = 6
Does 4(6) = 24? YES!
2) -6x = 18
Divide both sides by -6.
-6y = 18
y = -3
Does -6(-3) = 18? YES!

14. A fraction times a variable:
Ex: 2x = 4 3
Turn 4 into a fraction.
2x = 4
2. Cross Multiply.
2x = 12
Divide by 2.
x = 6
Ex: 3x = 7 6
Turn 7 into a fraction.
3x = 7
2. Cross Multiply.
3x = 42
Divide by 3.
x = 14

15. Try these on your own...