Pre-Algebra Chapter 1 - Ramsey School District

Most standardized tests include questions that ask you to solve equations.
Standardized
Test Practice
Example 2
Solve an Equation
Multiple-Choice Test Item
Which value is the solution of 2x 1 7?
A
6 B 5 C 4 D 3
Test-Taking Tip
The strategy of testing
each value is called
backsolving. You can also
use this strategy with
complex equations.
Read the Test Item
The solution is the value that makes the equation true.
Solve the Test Item Test each value.
2x 1 7 2x 1 7
2(6) 1 7 Replace x with 6. 2(5) 1 7 Replace x with 5.
13 7 11 7
2x 1 7 2x 1 7
2(4) 1 7 Replace x with 4. 2(3) 1 7 Replace x with 3.
9 7 7 7
Since 3 makes the equation true, the answer is D.
Example 3
Solve Simple Equations Mentally
Solve each equation mentally.
a. 5x 30
5 6 30 Think: What number times 5 is 30?
x 6 The solution is 6.
b. 7 2
8
d
7 2
8
9
Think: 72 divided by what number is 8?
d 9 The solution is 9.
Reading Math
Symmetric
Root Word: Symmetry
The word symmetry means
similarity of form or arrangement
on either side.
In Lesson 1-4, you learned that certain properties are true for any number.
Two properties of equality are shown below.
Properties of Equality
Property Words Symbols Example
If one quantity equals For any numbers If 10 4 6,
a second quantity, a and b, if a b, then 4 6 10.
Symmetric then the second then b a.
quantity also equals
the first.
Transitive
If one quantity equals For any numbers a, If 3 5 8
a second quantity and b, and c, if a b and and 8 2(4),
the second quantity b c, then a c. then 3 5 2(4).
equals a third
quantity, then the
first equals the third.
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Lesson 1-5 Variables and Equations 29