# Equations and Inequations

- An equation is statement that two algebraic expression are equal. It may involve one or more variables.
- An equation involving only first powers of one variable is called a simple equation or linear equation.
- To solve word problems, first you frame an equation corresponding to given problem and then solve this equation.
- Rules for solving inequations are similar to those for solving equations. However, when you divide or multiply both sides of an inequality by a negative number, the sign of inequality changes direction.

## Exercise

- Solve (2x +5)/2 - 5x / (5x - 1) = x
- Solve 2 + (2x -3)/(2x + 3) = (3x+4)/(x +2)
- Solve 0.5 (4x +1) = 0.3 (2x +1) +1.6
- Solve n -3 = 5n -15
- The difference between squares of two consecutive even integers is 92. Find the integers.
- The ages of A and B are in ratio 9:4. Seven years hence, the ratio of ages will be 5:3. Find their present ages.
- One half of a number is equal to one third of its succeeding number. Find the first number.
- In a shooting competition, a person receives 50 p if he hits the mark and pays 20 p if he misses it. He tried 60 shots and was paid Rs 1.30. How many times did he hit the mark?
- The angles of a triangle are in ratio 1:2:3. Find the angles. Classify the triangle.
- Represent the inequality -5 x < 5, x {even integers} on the number line.
- If x is an odd integer, then represent the solution set of inequality -5 x < 5 graphically.
- Solve the inequality 3 -x/2 > 2 -x/3, where x is a whole number.

## Answers

**1.**-1

**2.**-3

**3.**1

**4.**3

**5.**22, 24.

**6.**18 years, 8 years

**7.**2

**8.**19 times

**9.**30°, 60°, 90°; right angled triangle.

**10.**

**11.**

**12.**