Algebra II AB



Alg 2 BC U 1 Day 2 - Solving Equations and Inequalities

Goal: To solve equations/inequalities and compound inequalities;

To use equations/inequalities to solve word problems.

I. Solving equations: [pic]

II. Solving formulas for variables:

The formula for the area of a trapezoid is [pic]. Solve this equation for h.

Solve this same formula for [pic]: [pic]

Solve [pic]for x. State any restrictions on a and b.

III. Writing Equations to Solve Problems:

4-step Word Problem Format:

1)

2)

3)

4)

A dog kennel owner has 100 ft. of fencing to enclose a rectangular dog run. She wants it to be 5 times as long as it is wide. Find the dimensions of the dog run.

The lengths of the sides of a triangle are in the ratio 3:4:5. The perimeter of the triangle is 18 in. Find the lengths of the sides.

Two planes leave an airport at noon. One flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 miles apart after three hours. How fast was each plane flying?

(Hint: Use distance = rate*time and make a table!!!)

IV. Solving Inequalities:

*** REMEMBER: _____________________________________________________________ *** !!!

Interval Notation:

1. [pic]

2. [pic]

3. [pic]

V. Compound Inequalities: pairs of inequalities joined by “AND” or “OR”

5. Graph the solution of [pic]

Set Notation:

Interval Notation:

6. Graph the solution of [pic] (This is called a ______________ ________________.)

Set Notation:

Interval Notation:

7. Graph the solution of [pic]

Set Notation:

Interval Notation:

Word Problem: The sum of the lengths of any two sides of a triangle is greater than the length of the third. In triangle ABC, BC = 4 and AC = 8 –AB. Write an inequality for AB. (Hint: Let AB be represented by x.)

Extra Hint: You will need to use three inequalities to get a complete answer.

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AND: The solution is any value of x that makes BOTH equations true.

OR: The solution is any value of x that makes EITHER (or both) equation true.

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