Solve each of the following in equations and represent the solution se

1.	Solve each of the following in equations and represent the solution set on the number line. 3x – 7\|> 4, x ϵ R.
Answer» 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 ( \(\frac{11}{3}, \infty\))

Solve each of the following in equations and represent the solution set on the number line. 3x – 7|> 4, x ϵ R.

Answer»

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 ( \(\frac{11}{3}, \infty\))