1. Lesson 1: Solving Inequalities Using Addition and Subtraction

2. Bell Ringer: Solve the following equations. 1. x + 4 = 10 2. y – 5 = 9 3. 3 + t = 4 4. 8 = z + 4 5. 6 = y - 6 If you got the following: 1. x = 6 2. y = 14 3. t = 1 4. z = 4 5. y = 12 GREAT JOB!

3. Show me how you got the bell ringer To solve the previous problems, you must treat the equation like a balance. To solve #1 for x, you must subtract 4 from both sides of the equation. LIKE THIS: x + 4 = 10 -4 -4 -4 -4 x = 6 x = 6 #2) y – 5 = 9 #3) 3 + t = 4 #4) 8 = z + 4 #5) 6 = y – 6. +5 +5 -3 -3 -4 -4 +6 +6 y = 14 t = 1 4 = z 12 = y

4. Definition Inequality : An inequality is a mathematical sentence that contains a symbol; greater than (), less than (), less than or equal to greater than or equal to. Inequality : An inequality is a mathematical sentence that contains a symbol; greater than (>), less than (<), less than or equal to greater than or equal to. In which the terms on either side of the symbol are unequal (x 3). In which the terms on either side of the symbol are unequal (x 3).

5. Solving Inequalities Solving Inequalities are no different than solving equations; like in the bell ringer. 1. Solve for x. x+5<11 -5 -5 (solve by subtraction) -5 -5 (solve by subtraction) x<6 x<6 2. Solve for y. 2 > y – 4 +4 +4 (solve by adding) +4 +4 (solve by adding) 6 > y 6 > y

6. Some problem require you to write the inequality, then solve. Solve the following inequality; Five added to a number is at least eight. z +5 > 8 (choose any variable) -5 -5 -5 -5 z > 3 z > 3 *note: “at least” think of it’s meaning as z+5 is at least 8, which means it’s at smallest 8 but it could be larger. Therefore using the “greater than or equal” to symbol.

7. Try a few. 1. 3 > n – 2 2. z + 3 < 5 3. 4 less than a number is no more than 5. 4. The sum of a number and 4 is less than 6. 1. 6>n 2. Z<2 3. (n - 4 < 5) n<9 4. (n+4 <6) n < 2