You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
­3x
­3x
*get the variable on one side
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
­3x
­3x
7 > 2x ­ 6
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
­3x
­3x
7 > 2x ­ 6
+6
+6
*solve using inverse operations
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
­3x
­3x
7 > 2x ­ 6
+6
+6
13 > 2x
*solve using inverse operations
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
­3x
­3x
7 > 2x ­ 6
+6
+6
13 > 2x
2
2
*solve using inverse operations
You can solve an inequality with variables on both sides much like you solve an equation.
3x + 7 > 5x ­ 6
*solve using ­3x
­3x
inverse 7 > 2x ­ 6 operations
+6
+6
13 > 2x
2
2
1
1
or
x < 6 6 > x
2
2
Practice
8y > −2(3y − 7)
Practice
8y > −2(3y − 7)
*distribute
Practice
8y > −2(3y − 7)
8y > −6y +14
Practice
8y > −2(3y − 7)
8y > −6y +14
+6y
+6y
*get the variable on one side
Practice
8y > −2(3y − 7)
8y > −6y +14
+6y
+6y
14y > 14
Practice
8y > −2(3y − 7)
8y > −6y +14
+6y
+6y
14y > 14
14
14
*solve using inverse operations
Practice
8y > −2(3y − 7)
8y > −6y +14
+6y
+6y
14y > 14
14
14
y > 1
*solve using inverse operations
2(k – 3) > 6 + 3k – 3
2(k – 3) > 6 + 3k – 3
*distribute
*combine like terms
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
*get variable on one side
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
­k – 6 > 3 2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
­k – 6 > 3 + 6 +6
*solve using inverse operations
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
­k – 6 > 3 + 6 +6
­k > 9 *solve using inverse operations
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
­k – 6 > 3 + 6 +6
­k > 9 ­1 ­1
*solve using inverse operations
2(k – 3) > 6 + 3k – 3
2k – 6 > 3 + 3k
­ 3k
­ 3k
­k – 6 > 3 + 6 +6
­k > 9 *dividing by a ­1 ­1 negative reverses the k < ­9 inequality symbol!
Write and solve an inequality for the situation below.
Butler Landscaping will charge $150 plus $30 per hour to plant grass in Ms. Gonzales’ front yard. Boyle and Sons will charge $100 plus $40 per hour for the same job. After how many hours, h, is the amount that Boyle and Sons will charge more than what Butler Landscaping will charge?
any amount of time more than 5 hours
Butler Landscaping will charge $150 plus $30 per hour to plant grass in Ms. Gonzales’ front yard. Boyle and Sons will charge $100 plus $40 per hour for the same job. After how many hours, h, is the amount that Boyle and Sons will charge more than what Butler Landscaping will charge?
100 + 40h > 150 + 30h
­ 30h
­ 30h
100 + 10h > 150 ­ 100
­ 100
10h > 50 10
10
any amount of time h > 5
more than 5 hours
Write and solve an inequality for the situation below.
There are 45 boys and 61 girls signed up for camp. If an additional 5 boys and 3 girls sign up each day, when will the number of boys be greater than the number of girls?
There are 45 boys and 61 girls signed up for camp. If an additional 5 boys and 3 girls sign up each day, when will the number of boys be greater than the number of girls?
45 + 5d > 61 + 3d
­3d
­3d
45 + 2d > 61
­45
­45
2d > 16
2
2
d > 8
The number of boys signed up will be greater than the number of girls signed up when more than 8 days have elapsed.
Write and solve an inequality for the situation below.
Nick’s pond was stocked with 50 fish and an additional 5 fish are added each week. Mark’s pond was stocked with 15 fish and an additional 10 fish are added each week. Assuming no fish die or are removed, when will Mark’s pond have more fish in it than Nick’s?
Nick’s pond was stocked with 50 fish and an additional 5 fish are added each week. Mark’s pond was stocked with 15 fish and an additional 10 fish are added each week. Assuming no fish die or are removed, when will Mark’s pond have more fish in it than Nick’s ?
15 + 10w > 50 + 5w ­5w
­5w
15 + 5w > 50
­15
­15
5w > 35
5
5
w > 7
every week after 7 weeks have elapsed
Solve the inequality.
2 x + x + 4 < 5
9
3
6