Lesson 1:Lesson 1:Solving InequalitiesSolving Inequalities

Using Addition and Using Addition and SubtractionSubtraction

Bell Ringer: Bell Ringer: Solve the following equations.Solve the following equations.

1. x + 4 = 101. x + 4 = 10

2. y – 5 = 92. y – 5 = 9

3. 3 + t = 43. 3 + t = 4

4. 8 = z + 44. 8 = z + 4

5. 6 = y - 65. 6 = y - 6

If you got the following: 1. x = 62. y = 143. t = 14. z = 4

5. y = 12

GREAT JOB!

Show me how you got the bell ringer Show me how you got the bell ringer

To solve the previous problems, you must treat the To solve the previous problems, you must treat the equation like a balance.equation like a balance.

To solve #1 for x, you must subtract 4 from both To solve #1 for x, you must subtract 4 from both sides of the equation.sides of the equation.

LIKE THIS: LIKE THIS: x + 4 = 10 x + 4 = 10 -4 -4-4 -4

x = 6x = 6

#2) y – 5 = 9 #3) 3 + t = 4 #4) 8 = z + 4 #5) 6 = y #2) y – 5 = 9 #3) 3 + t = 4 #4) 8 = z + 4 #5) 6 = y – 6 . – 6 . +5 +5+5 +5 -3 -3 -3 -3 -4 -4-4 -4 +6 +6 +6 +6 y = 14 t = 1 y = 14 t = 1 4 = z 12 = y 4 = z 12 = y

DefinitionDefinition

Inequality Inequality : An inequality is a mathematical : An inequality is a mathematical sentence that contains a symbol; greater sentence that contains a symbol; greater than (than (>), less than (), less than (<), less than or equal ), less than or equal toto greater than or equal to. greater than or equal to.

In which the terms on either side of the In which the terms on either side of the symbol are unequal (x < y, 7 > 3). symbol are unequal (x < y, 7 > 3).

,

Solving InequalitiesSolving Inequalities

Solving Inequalities are no different than Solving Inequalities are no different than solving equations; like in the bell ringer.solving equations; like in the bell ringer.

1.1. Solve for x. x+5<11Solve for x. x+5<11 -5 -5-5 -5 (solve by subtraction) (solve by subtraction)

x<6x<6

2.2. Solve for y. 2 > y – 4Solve for y. 2 > y – 4 +4 +4+4 +4 (solve by adding) (solve by adding)

6 > y6 > y

Some problem require you to write Some problem require you to write the inequality, then solve.the inequality, then solve.

Solve the following inequality;Solve the following inequality;Five added to a number is at least Five added to a number is at least

eight.eight.z +5 z +5 >> 8 8 (choose any variable)(choose any variable)

-5 -5-5 -5 z z >> 3 3

*note: *note: “at least” think of it’s meaning as z+5 is at least 8, which means “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.it’s at smallest 8 but it could be larger. Therefore using the “greater than or Therefore using the “greater than or equal” to symbol.equal” to symbol.

Try a few.Try a few.

1.1. 3 > n – 23 > n – 2

2.2. z + 3 < 5z + 3 < 5

3.3. 4 less than a 4 less than a number is no more number is no more than 5.than 5.

4.4. The sum of a The sum of a number and 4 is number and 4 is less than 6.less than 6.

1.1. 6>n6>n

2.2. Z<2Z<2

3.3. (n - 4 (n - 4 << 5) 5)

nn<<9 9

4.4. (n+4 <6) (n+4 <6)

n < 2n < 2