I it is evident that 1 2 3 and 4 are the only natural numbers less than. 2 10 1 2 3 x 4 3 456 7 8 where the two lines overlap gives the solution as 2 10 1 2 3 x 3 456 exercises 1.

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### A x 1 b x 4 c 1 x 5 section 2 solving inequalities solving inequalities is similar to solving equations as in worksheet 2 2.

**Inequalities exercises pdf**. We may add or subtract numbers or algebraic terms from both or all sides of the inequality to isolate the variable from the rest of the expression. Solve each inequality below and illustrate the solution on a number line. Exercise 1 3 nesbitt s inequality let a b cbe positive real numbers prove the.

Ioi 0. Both inequalities can then be displayed as shown below. 2 1 basic elementary inequalities and their application exercise 1 2 let a b r prove the inequality a b b a 2.

121 2. Graph the following inequalities on number lines. A 4618x b 58 27x c 6737x d 57 17x e 26 4 1 x.

Exercises vii b find all x satisfying the given inequalities. I a if a20 algebraically la1 a if aso e g. Geometrically the absolute value of a real number a denoted la1 is the distance on a number line between 0 and a.

Equality occurs if and only if a b 0 i e. Solution from the obvious inequality a b 2 0wehave a2 2ab b2 0 a2 b2 2ab a2 b2 ab 2 a b b a 2. 2 the distance t between a and b.

Solve 24x 100 when i x is a natural number ii x is an integer answer the given inequality is 24x 100. 1 31 3 3. Class xi chapter 6 linear inequalities maths page 1 of 48 exercise 6 1 question 1.

Note that la bl is 1 31 3 121.

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