Question

Solve each of the following in equations and represent the solution set on the number line. 

5x + 2 < 17, where 

(i) x ϵ Z, 

(ii) x ϵ R.

Answer 1

(i) 5x + 2 < 17, x є Z 

Subtracting 2 from both the sides in the above equation, 

5x + 2 – 2 < 17 – 2 

5x < 15 

Dividing both the sides by 5 in the above equation,

\(\frac{5{\text{x}}}{5}\) < \(\frac{15}{5}\)

x < 3

Since x is an integer 

Therefore, possible values of x can be 

x = {…, -2, -1, 0, 1, 2}

(ii) 5x + 2 < 17, x є R 

Subtracting 2 from both the sides in above equation 

5x + 2 – 2 < 17 – 2 

5x < 15

Dividing both the sides by 5 in above equation

\(\frac{5x}{5} < \frac{15}{5}\)

x < 3 

Therefore, x є (-∞, 3)