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Lesson 7, Topic 2
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# Words Problems Leading to Inequalities

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### Example 1

If x is subtracted from 5 and the result is greater than 15. Find the range of values of x

Solution

x subtracted from 5

5 – x

Result > 15

$$\scriptsize 5 \: – \: x > 15$$

Collect like terms

$$\scriptsize 5 \: – \: x > 15$$

$$\scriptsize -x > 15 \: – \: 5$$

$$\scriptsize -x > 10$$

Divide both sides by -1 (reverse the sign)

$$\frac {-x}{-1} < \frac{10}{-1}$$

$$\scriptsize x < -10$$

Range of values of x :  -11, -12, -13, …

### Example 2

Olu is x years old. In 4 years time his age will still be less than 12 years.

(a) Write this information in an inequality in x

(b) Find the maximum age of Olu to the nearest whole number

Solution

(a) In 4 years time, Olu will be (x + 4) years

x + 4 is less than 12

$$\scriptsize x \: + \: 4 < 12$$

(b) Solve $$\scriptsize x \: + \: 4 < 12$$

collect like terms

$$\scriptsize x < 12 \: – \: 4$$

$$\scriptsize x < 8$$

Range of values of x:  7, 6, 5, 4, 3, …

Maximum age of Olu is 7 years

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