Page 53 - Math Course 1 (Book 2)

Solving Linear Equations

Your Turn! MO. 8 - L5b

Solve an Equation with Variables on Each Side Linear Equations:
No Solution or Identity
Solve 9f – 6 = 3f + 7.
1
A.
3
1
B.
12 Let’s Begin
1
C. 2
6
D. 2
No Solutions or Identity

Answer
Examples

A. Solve 8(5c – 2) = 10(32 + 4c).

Original
8(5c – 2) = 10(32 + 4c)
equation
Distributive
40c – 16 = 320 + 40c
Property
Subtract 40c
40c – 16 – 40c = 320 + 40c – 40c
from each side.
This statement
–16 = 320
Solve an Equation with Grouping Symbols is false.
3 Since –16 = 320 is a false
Solve 6(3r – 4) = (46r + 8) Answer
8 statement, this equation has
A. 38 no solution.
B. 28
C. 10
D. 36 1
.
B. Solve 4(t + 20) = (20t + 400)
5
1
4(t + 20) = (20t + 400) Original equation.
5
Answer 4t + 80 = 4t + 80 Distributive Property.

Since the expression on each
side of the equation is the same,
Answer this equation is an identity. The
statement 4t + 80 = 4t + 80
is true for all values of t.

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