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.
-----------------------
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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