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

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.

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

What if we see y + (-4) = 9? Check your solution! Does 13 - 4 = 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 = 9 +4 +4 y = 13

How about -16 + 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 +16 +16 z = 23 Check you solution! Does -16 + 23 = 7? YES! 7 = 7 and our solution is correct.

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.

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

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.

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

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.

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?

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

A fraction times a variable: Ex: 2x = 4 3 Turn 4 into a fraction. 2x = 4 3 1 2. Cross Multiply. 2x = 12 3. Divide by 2. 2 2 x = 6 Ex: 3x = 7 6 Turn 7 into a fraction. 3x = 7 6 1 2. Cross Multiply. 3x = 42 3. Divide by 3. 3 3 x = 14

Try these on your own...