Download Honors Algebra II

Honors Algebra II
Chapter 1 Notes
1.3- Solving an Equation
Rules to remember:
GOAL: Get variable ALONE
a. Get rid of parentheses first (Distributive property)
b. Add/Subtract like terms (ones with variable/ numbers w/out variables)
c. Divide/ Multiply to get variable alone
d. Check answers!!
**Remember to always use inverse operations!!**
Real-world ConnectionExample 1- A dog kennel owner has 100 feet 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.
Example 2- Adrian will use part of a garage wall as one of the long sides of a rectangular
rabbit pen. He wants the pen to be 3 times as long as it is wide. He plans to use 68 feet
of fencing. Find the dimensions of the pen.
Example 3- The lengths of the sides of a triangle are in the ratio 3:4:5. The perimeter of
the triangle is 18in. Find the lengths of its sides.
Example 4- The sides of a quadrilateral are in the ratio 1:2:3:6. The perimeter is 138 cm.
Find the lengths of the sides.
Example 5- Radar detected an unidentified plane 5000 miles away, approaching at
700mi/h. Fifteen minutes later an interceptor plane was dispatched, traveling at 800 mi/h.
How long did the interceptor take to reach the approaching plane?
Example 6- A plane takes off from an airport and flies east at a speed of 350mi/h. Ten
minutes later, a second plane takes off from the same airport and flies east at a higher
altitude at a speed of 400 mi/h. How long does it take the second plane to overtake the
first?
Example 7- A space probe leaves Earth at a rate of 3km/s. After 100 days, a radio signal
is sent to the probe. Radio signals travel at the speed of light, about 3 X 105 km/s. About
how long does the signal take to reach the probe?
1-4 Solving Inequalities
-Solve inequalities just like equations (same rules)
-To graph inequalities remember to shade number line in proper direction
(fill circle or no?)
-Flip sign of inequality if DIVIDING (OR MULTIPLYING) by a NEGATIVE
Compound Inequality- Connected by the word AND or OR
AND: BOTH PARTS MUST BE TRUE
OR: ONE OR THE OTHER MUST BE TRUE
1-5 Absolute Value Equations and Inequalities
The absolute value of a number is its distance from zero on the number line and its
distance in nonnegative.
a b  c
(Read as “the difference between “a” and “b” is “c”
ab  c
Read as “the difference between “a” and “opposite of b” is “c”
To solve an absolute value equation: “OR”
1. Get the absolute value alone on one side
2. Do both positive and negative value of OTHER side
3. You will get 2 solutions but CHECK BOTH (Extraneous Solution)Examples of Solving Absolute Value Equations:
a.
b.
c.
d.
Properties of Absolute Value Inequalities:
1. x  k is equivalent to x  k or x  k
2.
x  k is equivalent to  k  x  k
Examples of Absolute Value Inequalities:
a. x  k Example 1
b. x  k Example 2
c. x  k Example 1
d. x  k Example 2