Transcript Document

Unit 14
SIMPLE EQUATIONS
WRITING EQUATIONS

The following examples illustrate writing
equations from given word statements
 A number

less 15 equals 36:
Let n = the number
• The equation would become: n – 15 = 36 Ans
 Three
times a number plus 11 equals 20:
Let x = the number
 Three times the number would then be 3x

• The equation is now: 3x + 11 = 20 Ans
2
SUBTRACTION PRINCIPLE OF EQUALITY

The subtraction principle of equality
states:
 If
the same number is subtracted from both
sides of an equation, the sides remain
equal
 The equation remains balanced
3
SUBTRACTION PRINCIPLE OF EQUALITY

Procedure for solving an equation in
which a number is added to the
unknown:
 Subtract
the number that is added to the
unknown from both sides of the equation

Solve x + 7 = 12 for x:
x + 7 = 12
– 7 –7
x
= 5 Ans
4
ADDITION PRINCIPLE OF EQUALITY

Procedure for solving an equation in
which a number is subtracted from the
unknown.
 Add
the number, which is subtracted from
the unknown, to both sides of an equation
 The equation maintains its balance
5
ADDITION PRINCIPLE OF EQUALITY

Solve for p:
p – 19 = 42
+19 + 19
p = 61 Ans

Solve for y:
y – 43.5 = 6.79
+ 43.5 + 43.5
y = 50.29 Ans
6
DIVISION PRINCIPLE OF EQUALITY

Procedure for solving an equation in
which the unknown is multiplied by a
number:
 Divide
both sides of the equation by the
number that multiplies the unknown
 The equations maintains its balance
7
DIVISION PRINCIPLE OF EQUALITY
(Cont)

Solve for t: 9t = 18.9
9t 18.9

9
9
t = 2.1 Ans

Solve for x:-3.5x = 9.625  3.5 x  9.625
 3.5
 3.5
x = –2.75 Ans
8
MULTIPLICATION PRINCIPLE OF
EQUALITY

Procedure for solving an equation in
which the unknown is divided by a
number:
 Multiply
both sides of the equation by the
number that divides the unknown
 Equation maintains in balance
9
MULTIPLICATION PRINCIPLE OF
EQUALITY (Cont)

Solve for r:
r
5
3 .2
r
(3.2)  5 (3.2)
3 .2
r = 16 Ans
10
ROOT PRINCIPLE OF EQUALITY

Procedure for solving an equation in which
the unknown is raised to a power:
 Extract
the root of both sides of the equation
that leaves the unknown with an exponent of
1
 Equation maintains in balance
11
ROOT PRINCIPLE OF EQUALITY (Cont)

Solve for R: R3 = 27
3
R3 
3
27
R = 3 Ans
12
POWER PRINCIPLE OF EQUALITY

Procedure for solving an equation which
contains a root of the unknown:
 Raise
both sides of the equation to the
power that leaves the unknown with an
exponent of 1
 Equation maintains in balance
13
POWER PRINCIPLE OF EQUALITY
(Cont)

Solve for x:
5
x 5
 x  5
5
5
5
x = 3125 Ans
14
PRACTICE PROBLEMS

Express each of the following word problems as an
equation:
1.
2.

Four times a number minus 12 equals 36
Six subtracted from two times a number, plus three times
the number, equals fourteen
Solve each of the following equations:
3.
4.
5.
6.
7.
8.
9.
x + 7 = 22
n – 4.76 = 9.3
2/3m = 16
C  2.7 = 19.1
m + 9.1 = 16.3
x – 4/5 = 2/3
5.4y = 18.9
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PRACTICE PROBLEMS
10.
11.
p  4/5 = 7/12
121 = y2
16
 x2
25
 27 3
13.
c
64
14. c  12.4
12.
15.
3
x
4
5
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PROBLEM ANSWER KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
4x – 12 = 36
(2x – 6) + 3x = 14
15
14.06
24
51.57
7.2
1 7/15
3.5
7/15
11
4
12.
5
3
13.
4
14. 153.76
15.
64
125
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