2.3 Solving Word Problems

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2.3 Solving Word Problems
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Goals

• SWBAT solve linear inequalities
• SWBAT solve compound inequalities

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Solving Real World Problems

1. Carefully read the problem and decide what the
   problem is asking for.
2. Choose a variable to represent one of the unknown
   values.
3. Write an equation(s) to represent the
   relationship(s) stated in the problem. You may
   also need to draw a picture.
4. Solve the equation.
5. Check to see that your solution answers the
   question, if not, be sure to answer all parts.

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• 1. A landscaper has determined that together 1
  small bag of lawn seed and 3 large bags will
  cover 330 m2 of ground. If the large bag covers
  50 m2 more than the small bag, what is the area
  covered by each size bag?

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• 2. The length of one base of a trapezoid is 6 cm
  greater than the length of the other base. The
  height of the trapezoid is 11 cm and its area is
  165 cm2. What are the lengths of the bases?
• Hint the area of a trapezoid is

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• 3. Twice the sum of two consecutive integers is
  246. Let n the smaller integer.

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• 4. Each of the two congruent sides of an
  isosceles triangle is 10 cm shorter than its
  base, and the perimeter of the triangle is 205
  cm. Let x the length of the base.

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2.4 Solving Inequalities
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Notation

• The symbol is used to represent less than
• The symbol is used to represent less than or
  equal to
• The symbol is used to represent greater than
• The symbol is used to represent greater than
  or equal to

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Properties of Inequalities

• 1. If a, b, and c are real numbers, and if
  and , then
• 2. To solve inequalities, you can add or subtract
  the same number to both sides of the inequality
• If , then .
• 3. To solve inequalities, you can multiply or
  divide by the same number on both sides. However,
  if you multiply or divide both sides by a
  negative number, you the inequality.
• Example Multiply both sides of by -1 and
  see what happens!

flip
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Graphing Inequalities on a Number Line

• 1. Solve the inequality. Keep the variable on
  the left side of the equation.
• 2. If the inequality is lt or gt, use an
  circle. If the inequality is or use a
  circle.
• 3. Shade the number line in the direction that
  makes the inequality true. If you keep the
  variable on the left, you will shade in the
  direction the inequality points.

open
closed
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Solve the inequality and graph its solution set

• 1.

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Solve the inequality and graph its solution set

• 2.

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Solve the inequality and graph its solution set

• 3.

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Solve the inequality and graph its solution set

• 4.

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2.5 Compound Sentences
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• A sentence has either an or an .
• If the joiner is an that means that both
  sentences need to be true.
• If the joiner is an that means that only one
  sentence or the other needs to be true.

compound
and
or
and
or
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• For example, is the same this as saying
• and

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• Graphically, also written as
• and

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• So, the solution would look like

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• An or statement, on the other hand would look
  different since only ONE of the inequalities has
  to be true.
• For example, or
• Would 7 be a solution?
• Would 0 be a solution?
• Would 4 be a solution?

yes
yes
no
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• Graphically,
• or

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• So, the solution or would look like

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• When solving compound sentences where the
  variable is in the middle of two inequalities,
  set it up like an and problem to solve. Combine
  your inequalities into one statement at the end.
• When solving a compound sentence that is an or
  problem, solve each inequality and then graph
  them both.

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Solve the open sentence and graph its solution
set.

• 1.

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Solve the open sentence and graph its solution
set.

• 2.

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Solve the open sentence and graph its solution
set.

• 3.

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Solve the open sentence and graph its solution
set.

• 4. or

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Solve the open sentence and graph its solution
set.

• 5. or