1. Solving Inequalities by Adding or Subtracting
COURSE 3 LESSON 2-6
Solve p – 3 < –5.
p – 3 < –5 Notice that 3 is subtracted from p.
p – < –5 + 3 Add 3 to each side.
p < –2 Simplify.
Check
Step 1 See if –2 is a solution to the related equation.
p – 3 = –5 Write the related equation.
–2 – 3 –5 Substitute –2 for p.
–5 = –5 Simplify.
2-6

2. Solving Inequalities by Adding or Subtracting
COURSE 3 LESSON 2-6
(continued)
Step 2 Check the inequality symbol. Choose any number less than –2 and substitute it into the original inequality. In this case, try –3.
p – 3 < –5
–3 – 3 < –5
Substitute –3 for p.
–6 < –5
Steps 1 and 2 both check, so p < –2 is the solution of p – 3 < –5.
2-6

3. Solving Inequalities by Adding or Subtracting
COURSE 3 LESSON 2-6
After the hairdresser cut 3 in. from Rapunzel’s hair, her hair was at least 15 in. long. How long was her hair before she had it cut?
Let l = the length before cut.
Words length before cut – length cut is at least 15 in.
Inequality l –
> –
l – Notice that 3 is subtracted from l.
> –
l – Add 3 to each side.
> –
l Simplify.
> –
Rapunzel’s hair was at least 18 in. long before she had it cut.
2-6

4. Solving Inequalities by Adding or Subtracting
COURSE 3 LESSON 2-6
1. Graph x 6.
2. Write an inequality for k has a maximum of 4.
3. Solve r – 9 > 8.
< –
k 4
< –
r >17
2-6