FLC
Ch 7
Math 30 Prealgebra
Assume
and
Sec 7.1: Solving Equations Using One Principle of Equality
are real numbers.
Addition Principle of Equality
𝑎
𝑏⇒𝑎
Ex 1
𝑐
𝑏
𝑐
𝑎
𝑏⇒𝑎 𝑐
𝑏 𝑐
𝑎
b)
e)
𝑏⇒
c)
𝑎
𝑐
𝑏
𝑐≠
𝑐
d)
f)
g)
Solve each equation and check your solution.
a)
b)
c)
d)
(
Ex 3
Division Principle of Equality
To solve the equation, what principle must be applied? Solve the equation.
a)
Ex 2
Multiplication Principle of Equality
)
What does it mean when we say
(
is a solution to
)
?
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FLC
Ex 4
Ch 7
Sec 7.2: Solving Equations Using More Than One Principle of Equality
Solve each equation and check your solution. (Outline steps.)
a)
b)
d)
d)
e)
g)
c) Do this two ways
f)
(
h)
)
(
)
i)
j)
Ex 5
Sec 7.3: Solving Equations with Parentheses
Solve each equation and check your solution. (Outline steps.)
a)
b)
(
)
c)
(
)
(
)
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FLC
d)
(
Ch 7
)
(
e)
)
(
)
(
)
g)
)
(
(
)
h)
(
i) Do
f)
(
)
(
j) Do
)
(
)
)
Sec 7.4: Solving Equations with Fractions
How to Clear Fractions: MUST have an Equation (or Inequality)
1) Find the LCD of all fractions. You may need several factor trees.
2) Multiply each side of the equation by the LCD. You will likely need to distribute. (You’ll notice that when
doing this, just the numerator is multiplied by the LCD and the denominator is left alone, since it’s multiplied by .)
3) Simplify. All fractions should cleared. (Otherwise, we did something wrong.)
4) Solve the resulting equation. (Start by bringing all terms to one side and numbers to the other.)
5) Check your solution.
Ex 6
a)
Solve and check.
b)
c)
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Ch 7
d)
e)
(
Ex 7
f)
)
(
)
Simplify or solve.
a)
b)
(
)
(
)
Ex 8
Sec 7.5: Using Equations to Solve Applied Problems
(#4) If double a number is decreased by six, the result is eight. What is the number?
Ex 9
(#6)
If the sum of 8 and a number is multiplied by 6, the result is 54. What is the number?
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FLC
Ch 7
Ex 10
(#10)
Find the length of each side of the following triangle if the perimeter is 24 decimeters.
𝑥
𝑥
𝑥
Ex 11
(#16) Samantha is planning to enlarge a small rectangular space with length
so that the new area is
.
and width
a) How much should the length be enlarged?
b) What will the length of the enlarged space be?
Ex 12 (#18) Lena is a sales supervisor. The salesclerk earns $6200 less annually than Lena does. The
sum of Lena’s annual salary and the clerk’s annual salary is $58,000. How much does each earn?
a) Define the variable expressions.
b) Write an equation.
Start with ______________________________________.
Let
c) Solve the equation and determine the values asked for.
d) Check if your answer makes sense.
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FLC
Ch 7
Ex 13 (#28) A small community college has a total of 1704 students. 115 more students live on campus
than live in nearby off campus housing. 55 fewer students live at home and commute than live in
nearby off-campus housing. How many students are there in each of the 3 categories?
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