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**Answers to math exercises in 9th grade on solving inequalities**. Solve an inequation and represent the solution set on a graduated line in third grade.

Exercise 1:

Solve the following inequations:

a.

b.

c.

Exercise 2:

Solve the following inequalities:

1) .

2)

3)

4)

5)

6)

Exercise 3:

Let L be the length of this rectangle.

L > 5,3 cm

The perimeter of this rectangle is equal to : 2L + 2 × 5.3 = 2L + 10.6

2L + 10,6 ≤ 37

2L + 10,6 – 10,6 ≤ 37 – 10,6

2L ≤ 26,4

L ≤ 13,2

** Conclusion: the length of this rectangle is between 5.3 cm and 13.2 cm. **

Exercise 4:

Let x be the largest of three consecutive integers.

The previous one is equal to x – 1 and the smallest one is equal to x – 2.

The sum of these three integers is equal to : x – 2 + x – 1 + x = 3x – 3

12 < 3x – 3< 27

12 + 3 < 3x – 3 + 3 < 27 + 3

15 < 3x < 30

5 < x < 10

**The largest of these three integers is 6 , 7, 8 or 9.**

Exercise 5:

Represent on a graduated line the solutions of the inequation :

-2x+7 < 5x + 29.

Conclusion:

Exercise 6:

One amusement park offers two membership options:

**Formula A: ** The annual card costs 55 € and the price of an entry is 20 €.

**Formula B: ** The annual card costs 80 € and the price of an entry is 15 €.

We note y the number of entries .

1. Express, as a function of y, the cost per year with the formula A .

2. Express, as a function of y, the cost per year with the formula B .

3. From how many entries in the year, does formula B prove to be

the most interesting?

Formula B is the most interesting for less than 4 entries.

Exercise 7:

Consider the inequation:

1. Justify that 0 is a solution of this inequation.

or

** so 0 is the solution of this inequation. **

2. is it a solution of this inequation?

or

** so it is a solution of this inequation. **

3. After expanding the second member, solve this inequation.

The solutions are all numbers greater than -1.

**Remark:**

We verify that the two values

of the first questions are well overall solution.

## Answers to math exercises on inequalities in 3rd grade

After having consulted **the answers to these math exercises on solving inequalities** in 3rd grade, you can go back to the **exercises in 3rd grade**

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