LINEAR INEQUALITIES

IN ONE VARIABLE

1. Find the solution of each of the following inequalities!

a.

b.

c.

d.

e.

2. Sketch the graph of solutions of each of the following inequalities if x is a variable which takes on the numbers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 and 5!

a. x > 0

b. x £ 5

c. x > -3

d. x £ 0 and x > - 5

e.

3. Sketch the graph of solutions of each of the following inequalities if x is a variable which takes on the numbers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 and 5!

a. 6x + 9 £ 27

b. 3x + 4 <>

c. x – 5 > 3x – 1

d. 7 – 3x ≥ 2x – 3

e. 5 – 3x > 3x + 20

4. A kid traveled a distance of 9x km by bike, and then walked a distance of x km.

a. Find the total distance traveled in terms of x !

b. If the total distance was less than 30 km, form an inequality in x, and then solve it !

5. The figure on the left shows a square whose side is 4n cm long.

a. Find its perimeter in terms of n!

b. JIf the perimeter is less than 64 cm, form an inequality in n, and then solve it !

c. Find the substitutes for n if n is a variable which takes on the numbers 1, 2, 3, 4 and 5!

6. The lengths of the diagonals of a parallelogram are (2x -1) cm and (x +5) cm. If the first diagonal is longer than the second diagonal, form an inequality in x and solve it!

7. Look at the following triangle !

Every triangle holds the rule that the sum of the length of two sides is always greater than that of the third side. For the triangle ABC, AC + BC > AB. Form an inequality in x, and solve it!

8. Andi rode a bicycle at a speed of (x +3) km/hour for 1 hour and 15 minutes, and then at a speed of (2x – 4) km/hour for 1 hour and 30 minutes. If the total distance traveled was not greater than 19 km, form an inequality in x in the simplest form!

9.