Equation and Inequalities

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We can say equation is a statement that shows two mathematical expressions are equal in value. For example, x + 2 = 0. We can say inequation is also a statement that uses the symbols like > , <, ≥, ≤. We can use these symbols to indicate that one quantity is larger or smaller than other. 

Example 1: Solve for x: 6x – 14 = x + 11

Solution: The given equation is 6x – 14 = x + 11

We can add 14 on both sides

6x – 14 + 14 = x + 11 + 14

6x = x + 25

Now we can subtract x on both sides

6x – x = x + 25 – x

5x = 25

Divide by 5 on both sides of the above equation, we get, x = 5.

Example 2: Solve the inequality 7x – 6 ≤ 43

Solution: The given inequality is 7x – 6 ≤ 55

We can add + 6 on both sides of the inequation

7x – 6 + 6 ≤ 43 + 6

7x ≤ 49

Now we can divide by 7, then we get

So the solution of the given inequality is (-∞, 7].  Or

We can write this as x = {……….-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
 
Example3: Solve the inequality 3x +1 ≥ 13

Solution: The given inequality is 3x +1 ≥ 13

We can subtract 1 on both sides of the inequation

3x + 1 – 1 ≥ 13 – 1

3x ≥ 12

Divide by 3, Then we get x≥ 4

We can write the solution as x = {4, 5, 6, 7,……………………}



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