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Inequalities. Objective: Use inequalities. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12 7. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12 7 34 = 2s.

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## Inequalities

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**Inequalities**Objective: Use inequalities**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable.**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation.**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites.**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites. 700**5-Minute Check**• Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites. 700 • Check your solution.**Real Life Examples**• Inequalities are all around us! • What are some examples? Sliding pay scales Weight requirements Height requirements Speed limits Grades Capacity**From Words to Symbols**Inequality Symbols**Graphing Inequalities on a Number Line**• Steps: • Draw a number line • Put a circle around the number • If it includes “equal to” (£ , ³) fill in the dotRemember: Solid line, solid dot • Draw an arrow to the end of the number line making the statement true • Check your solution!**Example**• Graph x < 4 on a number line**Example**• Graph x < 4 on a number line When the variable is on the LEFT, the arrow points the same way as the inequality!**Like equations, inequalities can either be true or false**• Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15**When solving inequalities, do the same steps as solving**equations • Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 Plug it in!**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 Simplify!**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • Is 8 greater than 16? • This sentence is false.**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 Plug it in!**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 Simplify!**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 • 16 ³ 15**Example**• For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 • 16 ³ 15 • This sentence is true.**Compound Inequalities**• Compound inequalities are two inequalities considered together. • A compound inequality containing the word and is true only if both inequalities are true. This type of compound inequality is called a conjunction. • A compound inequality containing the word or is true if either of the inequalities is true. This type of compound inequality is called a disjunction.**Examples**• Examples of conjunctions: • x > -5 and x <1 • y < 3 and y > -3 • Examples of disjunctions: • x > -5 or x > 1 • y < 3 or y > -3**Writing Compound Inequalities**• When you see “and”, think of a sandwich! • x > -5 and x <1 is written -5 < x < 1 • y < 3 and y > -3 is written -3 < y < 3 • Hint: Graph each inequality separately, and see where they overlap!

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