Transcript Equation - Humble ISD

Exit Level
TAKS Preparation Unit
Objective 4
© A Very Good Teacher 2007
Writing Equations and Inequalities
• Identify if the situation warrants an
equation (=) or an inequality (<, >, ≤, ≥).
• Equations are used when quantities are
equal.
• Inequalities are used when quantities are
not equal.
Look for words like:
4, Ac3A
No more than
No less than
At least
At most
© A Very Good Teacher 2007
Writing Equations and Inequalities,
cont…
• Example: A used car salesman is paid a
salary of $200 per week plus at least a 10%
commission. If x represents the salesman’s
total sales, which of the following could be
used to determine y, the salesman’s weekly
income?
• Equation or Inequality?
income
Salary
+ Commission
The words “at least” Total
indicate
that this will
be an
inequality.
Now write the inequality.
y ≥
? 200 + .10x
Could be greater than or exactly
4, Ac3A
© A Very Good Teacher 2007
Solving Equations and Inequalities
• Write the equation or inequality (if necessary)
• Substitute any given values
• Remember to use inverse operations to
solve
• Example: Hanna makes necklaces that she sells at
a local craft show. She pays $50 a day to rent the
booth and each necklace costs $3.50 to make. If
she sells each necklace for $9, how many necklaces
does she need to sell to make a profit during a 3 day
weekend at the craft show?
1. Write the equation
Profit = 9x – (3.5x + 50(3))
4, Ac3B
© A Very Good Teacher 2007
Solving Equations and Inequalities, cont…
• Now that we have an equation, we can
substitute any given values
Profit = 9x – (3.5x + 50(3))
• We can replace ‘profit’ with zero to find the
break even point
0 = 9x – (3.5x + 50(3))
Now Solve 0 = 9x – 3.5x - 50(3)
0 = 9x – 3.5x - 150
0 = 5.5x - 150
+150
+150
27.27 = x
150 = 5.5x
5.5
5.5
4, Ac3B
© A Very Good Teacher 2007
Solving Equations and Inequalities, cont…
• The most important part of solving
equations involving word problems is
checking for reasonableness
• According to our equation x = 27.27
• Can Hanna sell 27.27 necklaces?
• So the answer must be a whole number
• Is it 27?
• No, selling 27 necklaces would not make a profit
• The answer is 28 necklaces!
4, Ac3B
© A Very Good Teacher 2007
Writing Systems of Equations
• Most systems are comprised of 2 types of
equations
• A total equation that represents the total number
of items
• And a comparison equation that represents the
relationship between the two variables
• Identify what the variables represent
• Identify which numbers go with each
equation type.
4, Ac4A
© A Very Good Teacher 2007
Writing Systems of Equations, cont…
• Example: Claudia purchased 12 shirts and jeans
for the school year. Jeans cost $22 and shirts
cost $15. If Claudia spent a total of $215, write a
system of equations that could be used to find the
number of shirts that Claudia purchased.
Total Equation
Comparison Equation
j + s = 12
22j + 15s = 215
4, Ac4A
© A Very Good Teacher 2007
Solving Systems of Equations
• The solution to a system of linear
equations is the point where the two lines
intersect.
• If you are unsure how to solve a problem by
substitution, elimination, or graphing, you
can substitute each answer choice into
the equations to see which one works for
BOTH equations.
4, Ac4B
© A Very Good Teacher 2007
Solving Systems of Equations, cont…
• Example: The equations of two lines are
4x – y = 3 and y = 5x – 2. What is the
value of x in the solution for this system of
equations?
y = 5x - 2
A. x = -2
B. x = -1
C. x = 2
D. x = 1
4x – y = 3
4(-2) – y = 3
-8 – y = 3
+8
+8
– y = 11
y = 5(-2) - 2
y = -10 - 2
y = -12
y = -11
Now try the other answers to see which one works for BOTH equations!
4, Ac4B
© A Very Good Teacher 2007