What you should learn

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What you should learn
Why you should learn it
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• VOCABULARY
• equation
• open sentence
• solution of an equation

formed when an equal sign is placed between two
expressions
an equation that contains at least one variable
a number which will make a true statement when
substituted for the variable in a single-variable
equation
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To check if a number is a possible solution to a
variable equation, simply substitute the number
for the variable. If the statement is true, the
number is a solution. If the statement is false,
the number is not a solution.
Checking a possible solution
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Extra Example 1
Check whether the numbers 3 and 4 are solutions
of the equation 5x 7 8.
x 3
5x 7 8
x 4 5x 7 8
5(4) 7 8
5(3) 7 8
8 8
13 ? 8
3 is a solution.
4 is not a solution.
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Extra Example 2
12(5) 5 125
12(10) 5 125
12(15) 5 125
65 ? 125
125 125
185 ? 125
Only 10 is a solution to the equation.
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• VOCABULARY
• solving an equation

finding all the solutions of an equation
For now, we will solve equations using mental
math.
Please work through the Activity on page 25.
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Extra Example 3
You need to buy ingredients to make a pizza.
Cheese costs 5.99, pizza dough costs 2.39,
tomato sauce costs 2.49, and pepperoni costs
2.98. You have a twenty-dollar bill. About how
much change will you receive? Work this out in
the best calculator you haveyour brain!
Hint Round each amount to the nearest
half-dollar.
Possible solution Rounding each amount gives 6
2.50 2.50 3 14. Subtracting gives 20
14 6. You will receive about 6 in change.
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Checkpoint

• Check whether the numbers 3, 6, and 9 are
  solutions of the equations 8s 20 52.
• 2. Use mental math to solve You need to buy
  supplies for school. A box of pencils costs
  2.98, a package of pens costs 3.95, a notebook
  costs 4.49, and a ruler costs 0.89. You have
  10. How much more money do you need?

9 is a solution 3 and 6 are not.
You need about 2.50.
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• VOCABULARY
• inequality
• solution of an inequality

formed when an inequality symbol is placed
between two expressions
a number which will make a true statement when
substituted for the variable in an inequality
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Inequality Symbols
Do you know how to read each of the four
inequality symbols? Lets find out! Match each
symbol with its meaning.
lt is greater than or equal to gt is less
than is less than or equal to is greater
than Click to see the answers.
To check if a number is a solution of an
inequality, simply substitute the number for the
variable. If it makes a true statement, the
number is a solution.
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Extra Example 4

• Decide whether 3 is a solution of the inequality.
• 3x 2 gt 5 b. x 5 lt 8
• c. x 1 2 d. 4x2 32

YES
NO
YES
NO
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Extra Example 5
If you weigh 120 lbs, the number of calories you
will burn while walking briskly is about 240
times the number of hours you walk. Using the
following values of x, will a 120 lb person
walking for x hours burn at least 500
calories? a. 2 hours b. 3 hours Hint
First, write a verbal model, then the
inequality. Model
Calories burned 500 Labels/Inequality
240 number of hours 500 240 t
500
Solution
b. 240t 500 240(3) 500 720 500 YES
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Checkpoint

• Decide whether 4 is a solution of the inequality.
• a. 2x 1 gt 5 b. x 2 gt 6
• c. x 3 5 d. 3x2 52
• Your scores on the last three tests were 82, 87,
  and 74. Your score on the next test is x points.
  Do the following values for x give you at least
  320 total points?
• a. 75 b. 81

NO
YES
YES
YES
NO
YES
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QUESTIONS?