Simplifying Linear Expressions through Subtraction
Ex. 1) Simplify.
(8x + 3) – (6x + 2)
Rewrite as adding
the additive inverse.
Rewrite vertically with
like terms in columns
.
Combine columns.
(8x + 3)
+
(
-
6x +
-
2)
8x + 3
+ -6x + -2
2x + 1
The subtraction sign in front of an expression in
parentheses means that you subtract EACH TERM in the
parentheses, not just the first term.
•
When subtracting expressions, we can rewrite the problem as
adding the opposite, or the additive inverse.
Ex. 2) Simplify.
(-6x + 1) – (2x – 5)
Rewrite as adding
the additive inverse.
Rewrite vertically with
like terms in columns
.
Combine columns.
(-6x + 1)
+
(
-
2x
+
5)
-6x + 1
+ -2x + 5
-8x + 6
Ex. 3) Simplify.
(-5x – 9) – (-6x – 1)
Rewrite as adding
the additive inverse.
Rewrite vertically with
like terms in columns
.
Combine columns.
(-5x – 9)
+
(
+
6x
+
1)
-5x + -9
+ 6x + 1
1x + -8
= 1x – 8
Ex. 4) Subtract (-2x + 5) from (-4x – 7).
Rewrite as adding
the additive inverse.
Rewrite vertically with
like terms in columns
.
Combine columns.
(-4x – 7)
+
(
+
2x +
-
5)
-4x + -7
+ 2x + -5
-2x + -12
= -2x – 12
(-4x – 7) – (-2x + 5)
Be careful with order as you
set up the subtraction problem!
Ex. 5) Simplify.
Rewrite as adding
the additive inverse.
Rewrite vertically with
like terms in columns
.
Combine columns.
Get common denominators
before adding fractions.
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4/9/2013
Note Page: Review of subtracting linear expressions
When subtracting linear expressions, it is essential to understand the concept of adding the additive inverse. By rewriting subtraction as addition, combining like terms vertically, and carefully manipulating signs, you can simplify expressions effectively. This process involves subtracting each term within parentheses and ensuring correct order when setting up subtraction problems. Practice and familiarity with these techniques will enhance your proficiency in simplifying linear expressions through subtraction.
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Presentation Transcript
Subtracting Linear Expressions
The subtraction sign in front of an expression in parentheses means that you subtract EACH TERM in the parentheses, not just the first term. When subtracting expressions, we can rewrite the problem as adding the opposite, or the additive inverse. Ex. 1) Simplify. (8x + 3) (6x + 2) Rewrite as adding the additive inverse. (8x + 3) + (-6x + -2) 8x + 3 Rewrite vertically with like terms in columns. + -6x + -2 2x + 1 Combine columns.
Ex. 2) Simplify. (-6x + 1) (2x 5) Rewrite as adding the additive inverse. (-6x + 1) + (-2x + 5) -6x + 1 Rewrite vertically with like terms in columns. + -2x + 5 -8x + 6 Combine columns.
Ex. 3) Simplify. (-5x 9) (-6x 1) Rewrite as adding the additive inverse. (-5x 9) + (+6x + 1) -5x + -9 Rewrite vertically with like terms in columns. + 6x + 1 1x + -8 Combine columns. = 1x 8
Ex. 4) Subtract (-2x + 5) from (-4x 7). Be careful with order as you set up the subtraction problem! (-4x 7) (-2x + 5) Rewrite as adding the additive inverse. (-4x 7) + (+2x + -5) -4x + -7 Rewrite vertically with like terms in columns. + 2x + -5 -2x + -12 Combine columns. = -2x 12
8 7 1 3 1 + + y y Ex. 5) Simplify. 8 2 6 + 8 6 7 1 3 1 Rewrite as adding the additive inverse. + + + y y 8 2 7 1 7 3 Rewrite vertically with like terms in columns. + y + y 8 2 8 6 = 3 1 3 1 + + y + + Get common denominators before adding fractions. y 8 6 8 6 10 2 + y 8 6 Combine columns. 1 1 = + 1 y 4 3
