Transcript PowerPoint - Professor John Wallace

Columbus State Community College
Chapter 2 Section 4
Solving Equations Using Division
Ch 2 Sec 4: Slide #1
Solving Equations Using Division
1. Solve equations using the division property of equality.
2. Simplify equations before using the division property of
equality.
3. Solve equations such as –x = 3.
Ch 2 Sec 4: Slide #2
Division Property of Equality
Division Property of Equality
If a = b, then
a
b
=
c
c
as long as c is not 0.
In other words, you may divide both sides of an equation by the same
nonzero number and still keep it balanced.
Ch 2 Sec 4: Slide #3
Equality Principle for Solving an Equation
Equality Principle for Solving an Equation
As long as you do the same thing to both sides of an equation, the
balance is maintained and you still have a true equation. (The only
exception is that you cannot divide by 0.)
Ch 2 Sec 4: Slide #4
Using the Division Property of Equality
EXAMPLE 1
Using the Division Property of Equality
Solve each equation and check each solution.
(a)
5n = 30
5n = 30
5
5
Check:
n = 6
5n = 30
5 · 6 = 30
Solution
30
Balance statement
= 30
Ch 2 Sec 4: Slide #5
Using the Division Property of Equality
EXAMPLE 1
Using the Division Property of Equality
Solve each equation and check each solution.
(b)
48 = –8x
48 = –8x
–8
–8
Check:
–6
= x
48 = –8x
48 = –8 · –6
Solution
48 = 48
Balance statement
Ch 2 Sec 4: Slide #6
CAUTION
CAUTION
Be careful to divide both sides by the same number as the coefficient
of the variable term. In Example 1 (b), the coefficient of –8x is –8,
so divide both sides by –8. (Do not divide by the opposite of –8,
which is 8. Use the opposite only when you’re eliminating a term.)
48 = –8x
–8
–6
–8
Divide both sides by
the coefficient –8.
= x
Ch 2 Sec 4: Slide #7
Simplifying before Solving Equations
EXAMPLE 2
Simplifying before Solving Equations
Solve each equation and check each solution.
(a)
2k – 6k = –14 – 6
Check:
2k – 6k
–4k
–4
k
2k – 6k
= –14 – 6
= –20
–4
= 5
= –14 – 6
2(5) – 6(5) = –20
10 – 30 = –20
–20
= –20
Solution
Balance statement
Ch 2 Sec 4: Slide #8
Simplifying before Solving Equations
EXAMPLE 2
Simplifying before Solving Equations
Solve each equation and check each solution.
(b)
2 – 8 = 11m – 9m
Check:
2 – 8
–6
2
–3
2 – 8
–6
–6
–6
= 11m – 9m
= 2m
2
= m
= 11m – 9m
= 11(–3) – 9(–3)
= –33 + 27
–6
=
Solution
Balance statement
Ch 2 Sec 4: Slide #9
Solving an Equation of the Type –x = 7
EXAMPLE 3
Solving an Equation of the Type –x = 7
Solve –x = 7 and check the solution.
–1
x = 7
–1
Check:
x
–1 x
–1(–7)
7
–1
=
=
=
=
–7
Solution
7
7
7
Balance statement
Ch 2 Sec 4: Slide #10
CAUTION
CAUTION
As the last step in solving an equation, do not leave a negative sign in
front of a variable. For example, do not leave –x = –9. Write the
understood –1 as the coefficient so that
–x
= –9
is written as
–1x
= –9.
Then divide both sides by –1 to get x = 9. The solution is 9.
Ch 2 Sec 4: Slide #11
Solving Equations Using Division
Chapter 2 Section 4 – Completed
Written by John T. Wallace
Ch 2 Sec 4: Slide #12