Page 179 - ArithBook5thEd ~ BCC

which can be reorganized, by associativity of addition, to

5x +(−11x)+ (−4y)+ 3y +2t =[5 + (−11)]x +[−4+ 3]y +2t
= −6x +(−1y)+ 2t
= −6x − y +2t.

At the final step, we revert to subtraction.

6.4.1 Exercises

Simplify the expressions by combining like terms.

1. 2x +9x

2. −3c +14c − 19c − d

3. 3x − 2y +11x − 9y

1 3
4. x − x
2 4
5. a − b +2a − c +2b

6. 1.09x − 0.07x

7. 1.2y +3.03y − 50y

1 3 2
8. 3x + y − x − z − x +2z
2 2 3

6.5 Linear Equations in One Variable

An equation is a statement that two mathematical expressions are equal. If the statement has just one
variable, and if

• the variable does not appear in the denominator of a fraction,

• the variable does not appear under a √ symbol,

• the variable is not raised to a power other than 1,

then we have a linear equation in one variable. Here are some examples of linear equations in one
variable:
2
2x +4 = 8 − 3y =12 z − 9= −1 2 − t =0.
3
Note that a linear equation contains only linear terms, constants and the equality symbol.
A solution to an equation in one variable is a number which, when substituted for the variable,
makes a true statement.
Example 225. Show that −4is a solution to the equation −3y =12

Page 179