2.3 Solving Word Problems

Goals SWBAT solve linear inequalities SWBAT solve linear inequalities SWBAT solve compound inequalities SWBAT solve compound inequalities

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.

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?

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? 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 Hint: the area of a trapezoid is

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

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.

2.4 Solving Inequalities

Notation The symbol is used to represent “less than” 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 “less than or equal to” The symbol is used to represent “greater than” The symbol is used to represent “greater than” The symbol is used to represent “greater than or equal to” The symbol is used to represent “greater than or equal to”

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

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, 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

Solve the inequality and graph its solution set 1.

2.

3.

4.

2.5 Compound Sentences

A sentence has either an or an. 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 both sentences need to be true. If the joiner is an that means that only one sentence or the other needs to be true. If the joiner is an that means that only one sentence or the other needs to be true. compound andor and or

For example, is the same this as saying and

Graphically, also written as Graphically, also written as and and

So, the solution would look like

An or statement, on the other hand would look different since only ONE of the inequalities has to be true. An or statement, on the other hand would look different since only ONE of the inequalities has to be true. For example, or For example, or Would 7 be a solution? Would 7 be a solution? Would 0 be a solution? Would 4 be a solution? yes no

Graphically, or or

So, the solution or would look like

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 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. When solving a compound sentence that is an or problem, solve each inequality and then graph them both.

Solve the open sentence and graph its solution set. 1.

2.

3.

4.or

Solve the open sentence and graph its solution set. 5.or