Sec. 2.1 Equations and Formulas
An equation is 2 variable pressions .html">expressions set equal to each other. To solve an
equation , find the value for the variable that makes the equation true.
To check an equation, evaluate the expressions. Determine if the result is a
true statement.
Checking Equations
1. Is 4 a solution of 3y – 4 = 2y?
2. Is -1 a solution of y^2 – 1 = 4y – 3?
Identities
An identity is an equation that is always true, such as
x + 3 = 3 + x.
Determine if the equations be low are identities :
3. 2(x + 3) + 4 = 2x + 10
4. 3x – 27 = 3(x – 7) + 6
Using Geometric Formulas
Recall these ideas from geometry:
Perimeter – the distance around a geometric figure
The perimeter of a circle is called the circumference.
Area – the measure of the surface within a geometric figure
Volume – the measure of the capacity within a 3-dimensional
figure
Solve these problems using geometric formulas:
1. Find the area of a trapezoid if the bases measure 8 cm
and 10 cm, and the height is 12 cm.
2. Find the volume of a c one if the radius is 7 in and the
height is 10 in.
3. Baseboards are being installed around a room that
measures 12 ft by 18 ft. There are two 3ft wide doors in
the room. If baseboard costs $2.80 per foot, find the
cost of the baseboard. P=2L+2W
4. The walls of a room measuring 14 ft by 12 ft are being
painted. The walls are 8 ft. tall. There are two windows
in the room, each 3 ft by 4 ft. Calculate the total square
feet to be painted. A=L*W
Using Other Formulas
Distance
Temperature
3. Joan left home at 8:30 am to travel to Cleveland, a
distance of 150 miles. She arrived at 11:45 am, having
stopped once for 30 minutes to pick up some groceries.
Find her average rate of travel.
4. The temperature on the bank sign reads 24°C. Is it cold
outside? Convert 24°C to Fahrenheit.
Sec. 2.2 Solving Equations Using the Addition Principle
To find the solution to an equation, we may add (or subtract) the same number
to each side of the original equation.
Solve:
1. b – 4 = 11
2. b – 4.06 = 11.59
3. x + 7 = 20
5. 9 + x = -3
6. 4 = m – 11
7. 13 = -6 + a
10. w + 2.932 = 4.801
11. 5w + 6 – 4w = 8
12. 6(B + 2) – 5B + 1 = 6
To solve these equations, first get the variable terms on the same side by
using the addition principle.
13. 3x + 5 = 2x + 9
14. 5w – 7 = 4w – 9
Contradictions
A contradiction is an equation with no solution such as
3x – 4 = 3x + 5.
Show that this equation is a contradiction:
2(x – 1) + 3x = 5x + 1
Application Problems
Write an equation (top priority here!) and solve the problem:
1. Joanna is planning to buy a new car. She needs a down payment of $3450. If
she has already saved $2690, how much more does she need?
2. The perimeter of a triangle is 38 in. If two sides measure 17 in and 9 in,
find the length of the 3rd side.
Sec. 2.3 Solving Linear Equations Using Multiplication
To solve an equation, we may multiply ( or divide ) both
sides
of an equation by the same number.
Solve:
1. -5m = 20
2. 18 = 0.2t
3. -56 = 7x
4. -1/6N = -30
9. 2.31m = 2.4255
10. 2x – 5x = 9
These next equations require the application of both the
addition and multiplication principles . Apply the addition principle first!
11. 3n – 7 = -19
12. 5 – 6x = -13
13. 3 = 11 – 4n
14. -3x + 19 = 19
15. 9 = -12c + 5
16. 8 = 7d – 1
17. 4 – 3/4 z = -2
18. 2x – 6x + 1 = 9
19. 6y + 2 = y + 17
20. m + 4 = 3m + 8
21. 3 – 2y = 15 + 4y
22. 3x + 2(x – 1) = 8
23. 8m – 5(m – 2) = 7
24. 8 – 7x = 14 – (5x + 6)
25. 0.11x + .14(8000 – x) = 1015
Application Problems
26. The perimeter of a rectangle is 35.4 cm when the
length
is 13.5 cm. Find the measure of the width. P=2L+2W
27. The area of a trapezoid is 88 sq. in. when the height
is
8 in. and one base measures 15 in. Find the measure of
the other base. 
Sec. 2.4 Rewriting Formulas
We can use equation-solving principles to rewrite formulas
in terms of another variable.
1. Solve P = 4s for s.
2. Solve A = B – C for B.
3. Solve A = B – C for C.
4. Solve A = 1/2bh for b.
5. Solve 2x + 3y = 6 for x.
6. Solve 4x – 5y = 10 for y.
7. Solve 3x – y + 12 = 0 for x.
8. Solve P = 2L + 2W for W.
9. Solve F = 9/5C + 32 for C.
10. Solve A = 1/2h(a + b) for a.
11. Solve 
for r.
12. Solve 
for G.
Sec. 2.5 Translating Word Sentences Into Equations
Phrases that Translate into Equals
"is equal to", "results in", "is", "is the result", "is
the same as"
Translate these word sentences into equations and then
solve to find the number
1. Five more than four times a number is thirteen.
2. Eight less than three times a number is equal to seven.
3. Twenty-one more than triple a number is fifty-four.
4. If two added to the quotient of a number and three, the
result is eight.
5. Five times a number is equal to eighteen more than
twice the number.
6. Four times the sum of a number and three equals two
less than five times the number.
7. The product of six and four more than a number is equal
to eleven subtracted from the number .
8. One half the sum of a number and four is equal to two
less than the number.
Find the mistake(s) made in translating the phrases below:
9. "Three times the sum of a number and 5 is twenty-one"
was translated as 3x + 5 = 21.
10. "The product of seven less than a number and five is
equal to negative twenty -five" was translated as 5(7 – x) = 25.
