Chapter 5 - Solving for the unknown: a how-to approach for solving equations. After you have mastered the material in this chapter, you will be able to: Explain the basic procedures used to solve equations for the unknown; list the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers; list the steps for solving word problems; complete blueprint aids to solve word problems; check the solutions.
Trang 1Solving for the Unknown: A
Howto Approach for Solving Equations
Trang 21 Explain the basic procedures used to
solve equations for the unknown
2 List the five rules and the mechanical
steps used to solve for the unknown in seven situations; know how to check the answers
Solving for the Unknown: A howto Approach for Solving Equations
#5
Learning Unit Objectives
Solving Equations for the Unknown
LU5.1
Trang 31 List the steps for solving word problems
2 Complete blueprint aids to solve word
problems; check the solutions
Solving for the Unknown: A howto Approach for Solving Equations
#5
Learning Unit Objectives
Solving Word Problems for the Unknown
LU5.2
Trang 4numbers and letters called terms.
Equation – A mathematical statement with an equal sign showing that a mathematical
expression on the left equals the mathematical expression on the right
Formula – An equation that expresses in symbols
a general fact, rule, or principle.
Terminology
Trang 5Left side of equation Right side of equation
Equality in equations
Dick’s age in 8 years will equal 58
Trang 61. If no number is in front of a letter, it is a
1: B = 1B; C = 1C
2. If no sign is in front of a letter or
number, it is a +: C =
+C; 4 = +4
Trang 7Whatever you do to
one side of an equation, you must do
to the other side.
Trang 8If an equation indicates a process such as addition, subtraction, multiplication, or division, solve for the unknown or variable
by using the opposite
process.
Trang 9A + 8 = 58 8 8
A = 50
Check
50 + 8 = 58
Trang 10You can add the same quantity or number to both sides of the equation and subtract the same quantity or number from both sides of the equation without affecting the equality of the equation. You can also divide or multiply both sides of the equation by the same quantity or number (except 0) without affecting the equality of the equation.
Trang 117G = 35 7G = 35
7 7
G = 5
Check
7(5) = 35
Trang 12When solving for an
unknown that involves more than one process, do the
addition and subtraction before the multiplication and
division.
Trang 13H + 2 = 5 4
H + 2 = 5 4
2 2
H = 3 4
H = 4(3) 4
H = 12
( )
(4)
Check
12 + 2 = 5
4
3 + 2= 5
Trang 14When equations contain parentheses (which indicates grouping together, you solve for
the unknown by first multiplying each item inside the parentheses by the number or
letter just outside the parentheses. Then you continue
to solve for the unknown with the opposite process used in the equation. Do the addition and subtractions first; then the multiplication and division.
Trang 155(P 4) = 20 5P – 20 = 20 +20 +20
5P = 40 5P = 40
5 5
P =8
Check
5(84) = 20
5(4) = 20
20 = 20
Trang 16To solve equations with like unknowns, you first combine the unknowns and then
solve with the opposite process used
in the equation.
Trang 174A + A = 20 5A = 20 5A = 20
5 5
A = 4
Check
4(4) +4 = 20
16 + 4 = 20
Trang 181) Read the entire Problem
2) Ask: “What is the
problem looking for?”
3) Let a variable
represent the unknown
4) Visualize the
relationship between the unknowns and variables. Then set up
an equation to solve for unknown(s)
Y = Computers
4Y + Y = 600
Read again if necessary
Trang 19Unknown(s) Variable(s) Relationship
Blueprint aid
Trang 20ICM Company sold 4 times as many computers as Ring Company. The difference in their sales is 27. How many computers of each company were sold?
4C C = 27 3C = 27
Ring = 9 computers ICM = 4(9) = 36 Computers
Cars Sold
ICM 4C 4C Ring C C
27