Question

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

3x – 7|> 4, x ϵ R.

Answer 1

Given: 

|3x – 7|> 4, x ϵ R. 

3x – 7 < -4 or 3x – 7 > 4 

(Because |x| > a, a>0 then x < -a and x > a) 

3x – 7 < -4 

Now, adding 7 to both the sides in the above equation 

3x – 7 + 7 < -4 +7 

3x < 3 

Now, dividing by 3 on both the sides of above equation

\(\frac{3{\text{x}}}{3} < \frac{3}{3}\)

x < 1 

Now, 3x – 7 > 4 

Adding 7 on both the sides in above equation 

3x – 7 + 7 > 4 + 7 

3x > 11 

Now, dividing by 3 on both the sides in the above equation

\(\frac{3x}{3} > \frac{11}{3}\)

x > \(\frac{11}{3}\)

Therefore,

x ∈ (-∞ , 1) U ( \(\frac{11}{3}, \infty\))