Objectives: Solve one-step equations using multiplication or division.

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Presentation transcript:

Objectives: Solve one-step equations using multiplication or division.

Inverse Operations To solve equations we isolate (get by itself) variables by using inverse operations. The following needs to be memorized: Inverse Operations Addition Subtraction Multiplication Division Square x2 Square Root

Steps to solving ALL equations Clear parenthesis (Use distributive Property) Combine Like Terms on each side of the = Move all variables to one side of the “=“ using inverse operations (+ or -) Move all constants (numbers) to the other side of the “=“ using inverse operations (+ or -) Get rid of the constant (number) attached to the variable by either (x or ÷)

j –8 = 3 Solve the equation n 1. 2. = 2.8 6 n = 16.8 –24 = j 3. 4. 1. 2. n = 16.8 –24 = j 3. 4. 9y = 108 16 = 4c y = 12 4 = c

Solve the equation –13 = y 3 5. 6. 0.5y = –10 y = –20 –39 = y = 7 c 8 15k = 75 7. 8. k = 5 c = 56

Objectives: Solve one-step inequalities using multiplication and division.

All inequalities have an infinite number of solutions. REMEMBER: All inequalities have an infinite number of solutions. ANY number that falls on the arrow is considered a solution. Example: –4 –3 –2 –1 1 2 3 4 5 6 Solutions: 0, -1, -2, -3, -1000, -10,000,000… NOT solutions: 1, 2, 3, 4, 5, ….

The following symbols need to be memorized…. When graphing inequalities the symbol tells you what type of dot you should have. Hint: If there is a solid line under the symbol you should have a solid dot!

Before graphing an inequality make sure that your variable is on the LEFT side. If this is true the arrow should point in the same direction as the symbol. Symbol points LEFT, Arrow points LEFT Symbol points RIGHT, Arrow points RIGHT

The only difference between solving equations and inequalities is: WHEN SOLVING INEQUALITIES… IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER YOU MUST FLIP THE SIGN!!!!!

9. 10. Solve the inequality. Graph the solution. 3(2.4) ≤ 3 7.2 ≤ m 9. 10. 3(2.4) ≤ 3 7.2 ≤ m (or m ≥ 7.2) 2 4 6 8 10 12 14 16 18 20

-2x ≥ 10 11. 12. 7x > –42 Solve the inequality. Graph the solution. 11. 12. 7x > –42 -2x ≥ 10 > x > –6 –10 –8 –6 –4 –2 2 4 6 8 10

4k > 24 50 ≥ -5q 13. 14. Solve the inequality. Graph the solution. 13. 14. 4k > 24 50 ≥ -5q k > 6 2 4 6 8 10 12 16 18 20 14