Transcript 2.3 Solving Word Problems

2.3 Solving Word
Problems
Goals

SWBAT solve linear inequalities

SWBAT solve compound inequalities
Solving Real World Problems
1.
2.
3.
4.
5.
Carefully read the problem and decide
what the problem is asking for.
Choose a variable to represent one of the
unknown values.
Write an equation(s) to represent the
relationship(s) stated in the problem. You
may also need to draw a picture.
Solve the equation.
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?
Hint: the area of a trapezoid is
1
A  h b1  b2 
2
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 or equal to”
The symbol
is used to represent
“greater than”
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
b  c then a  c
ab
and ,
2. To solve inequalities, you can add or subtract the
same number to both sides of the inequality:
If a  b , then a  c  b  c .
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,
flip
you
the inequality.
Example: Multiply both sides of 2  6 by -1 and
see what happens!
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 < or >, use an open
circle. If the inequality is  or  use a
closed
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.
Solve the inequality and
graph its solution set
1.
2a  1  13
Solve the inequality and
graph its solution set
2.
1
11
 n  5  
3
3
Solve the inequality and
graph its solution set
3.
6 1  2h   7h  9
Solve the inequality and
graph its solution set
4.
2 4  5v 
35v  6 
1 
1
3
2
2.5 Compound
Sentences

A
compound
and


or an
sentence has either an
or
.
If the joiner is an and that means that
both sentences need to be true.
If the joiner is an or that means that
only one sentence or the other needs to
be true.
3 x 7
For example,
this as saying
3 x
and
x7
is the same

Graphically,
3 x
also written as
3
7
and
x7
3
7
x3
So, the solution
like
3
3  x  7 would look
7


An or statement, on the other hand would
look different since only ONE of the
inequalities has to be true.
For example,
x6
Would 7 be a solution?
or
x2
yes
Would 0 be a solution?
yes
Would 4 be a solution?
no
Graphically,
x6
2
6
or
x2
2
6
So, the solution x  6
would look like
2
or x  2
6


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.
Solve the open sentence and
graph its solution set.
1.
 3  2d  1  7
Solve the open sentence and
graph its solution set.
2.
1
6  9  t  10
2
Solve the open sentence and
graph its solution set.
3.
4  y 7  3y
1  11y

 2 
5
2
10
Solve the open sentence and
graph its solution set.
4.
4d 3
7
or
5
5
d
1  4
2
Solve the open sentence and
graph its solution set.
5.  11  4v  3  5 or
v  5  7  2v  3