Solving Inequalities Using
Addition or Subtraction
Common Core State Standards
A-REI.B.3 Solve linear equations and inequalities
in one variable, including equations w ith coefficients
represented by letters. Also A-CED.A.1
MP 1, MP 2, MP 3, MP 4Ob ject ive To use addition or su b tractio n to solve inequalities...Getting Ready!Make sure you
understand the
problem. W hich
numbers do you
need to use?MATHEMATICAL
PRA CTICESIn a U .S. presidential election, a candidate
must win at least 270 out of 538 total
elect o ral vot es t o be d eclared t he winner.
Su p p o se a c a n d i d a t e h a s e a r n e d 2 3 8
elect o ral vot es in st at es out side t he
so u t h east er n U .S.
What is the least number of states in the
so u t h east er n U. S. t h a t t h e can d i d at e co uld
win and st i l l b ecom e p r esi d en t? W h at ar e
these states? Justify your reasoning.So u t h east er n Un i t ed St at es
DC 3 DE 3
It- M D10Lesso n i
Vocabulary
equivalent
inequalities
You can m odel the situation in th e Solve It w ith th e inequality 238 + x > 270, w here x
represents th e n u m b e r of electoral votes n eed ed. You can find its solutions using one of
the properties o f inequality.Essential U nderstanding Just as you u sed properties of equality to solve
equations in C hapter 2, you can use p roperties of inequality to solve inequalities.
The A ddition Property of Inequality is show n below. Applying this p roperty to an
inequality pro d u ces an equivalent inequality. Equivalent inequalities are inequalities
that have the same solutions.Key Concept Addition Property of Inequality
Words
Let a, b, an d c be real num bers.
If a > b, then a + c > b + c.
If a<b, then a + c < b + c.
This p roperty is also tru e for > an dExam ples
5 > 4, so 5 + 3 > 4 + 3.- 2 < 0 ,so - 2 + 1 <0 + 1.
Diagram
The diagram below illustrates one way to
th in k a b o u t this rule.
+c +cI
Po w erAlg eb ra.com | Lesso n 3-2 So l v i n g I n e q u a l i t i e s U s i n g A d d i t i o n o r Su b t r a c t i o n j 1 7 1