Solving inequalities Key concept Solving inequalities Key concept

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Solving inequalities: Key concept:

Solving inequalities: Key concept:

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign.

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign.

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition Property of Inequality:

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition Property of Inequality: ◦ You can add any number to an inequality, as long as you add the same number to BOTH sides.

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition Property of Inequality: ◦ You can add any number to an inequality, as long as you add the same number to BOTH sides. X– 4>6

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition Property of Inequality: ◦ You can add any number to an inequality, as long as you add the same number to BOTH sides. X– 4>6 + 4 +4

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Addition Property of Inequality: ◦ You can add any number to an inequality, as long as you add the same number to BOTH sides. X– 4>6 + 4 +4 X > 10

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction Property of Inequality:

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction Property of Inequality: ◦ You can subtract any number from an inequality, as long as you subtract the same number from BOTH sides.

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction Property of Inequality: ◦ You can subtract any number from an inequality, as long as you subtract the same number from BOTH sides. X+4>6

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction Property of Inequality: ◦ You can subtract any number from an inequality, as long as you subtract the same number from BOTH sides. X+4>6 - 4 -4

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Subtraction Property of Inequality: ◦ You can subtract any number from an inequality, as long as you subtract the same number from BOTH sides. X+4>6 - 4 -4 X>2

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense.

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense. Since X > 2, pick a number larger than 2, like 5

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense. Since X > 2, pick a number larger than 2, like 5 X+4>6

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense. Since X > 2, pick a number larger than 2, like 5 X+4>6 5+4>6

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense. Since X > 2, pick a number larger than 2, like 5 X+4>6 5+4>6 9>6

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check

Solving inequalities: Key concept: ◦ Treat the inequality EXACTLY like an equals sign. Check your answer by substituting in a value that makes sense. Since X > 2, pick a number larger than 2, like 5 X+4>6 5+4>6 9>6 True

Solving inequalities: Solve and then graph the solution. Be sure to check your solution.

Solving inequalities: Solve and then graph the solution. Be sure to check your solution.

Solving inequalities: Solve solution. and then graph the

Solving inequalities: Solve solution. and then graph the

Solving inequalities: Key concept:

Solving inequalities: Key concept:

Solving inequalities: Key concept: ◦ If you switch the sides of the equation, you

Solving inequalities: Key concept: ◦ If you switch the sides of the equation, you have to switch the inequality.

Solving inequalities: Key concept: ◦ If you switch the sides of the equation, you

Solving inequalities: Key concept: ◦ If you switch the sides of the equation, you have to switch the inequality.

Solving inequalities: Multiplication Property of Inequality:

Solving inequalities: Multiplication Property of Inequality:

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides.

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you multiply by a NEGATIVE number you must FLIP the inequality.

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you multiply by a NEGATIVE number you must FLIP the inequality. ◦ X<7 -2

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you multiply by a NEGATIVE number you must FLIP the inequality. ◦ X<7 -2 To cancel the division you multiply.

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you multiply by a NEGATIVE number you must FLIP the inequality. ◦ X<7 -2 To cancel the division you multiply.

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any

Solving inequalities: Multiplication Property of Inequality: ◦ You can multiply an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you multiply by a NEGATIVE number you must FLIP the inequality. ◦ X<7 X > -14 -2 To cancel the division you multiply. Since you multiplied by a negative, you have to flip the inequality.

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any number as long as you do it to BOTH sides.

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you divide by a NEGATIVE number you must FLIP the inequality.

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you divide by a NEGATIVE number you must FLIP the inequality. ◦ -2 X < 10

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you divide by a NEGATIVE number you must FLIP the inequality. ◦ -2 X < 10 -2 -2

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any

Solving inequalities: Division Property of Inequality: ◦ You can divide an inequality by any number as long as you do it to BOTH sides. ◦ HOWEVER, if you divide by a NEGATIVE number you must FLIP the inequality. ◦ -2 X < 10 -2 -2 X > -5

Solve and then graph the solution to the following inequalities. Be sure to check

Solve and then graph the solution to the following inequalities. Be sure to check your solution.

Assignment: Page 208 -209 Numbers # 4 -20, 24 -38, 46 -50 Even

Assignment: Page 208 -209 Numbers # 4 -20, 24 -38, 46 -50 Even