Question

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

5 – 2x| ≤ 3, x ϵ R.

Answer 1

Given: 

|5 – 2x| ≤ 3, x ϵ R. 

5 – 2x ≥ - 3 or 5 – 2x ≤ 3 

5 – 2x ≥ -3 

Subtracting 5 from both the sides in the above equation 

5 – 2x – 5 ≥ - 3 – 5 

-2x ≥ - 8 

Now, multiplying by -1 on both the sides in the above equation 

-2x(-1) ≥ -8(-1) 

2x ≤ 8 

Now dividing by 2 on both the sides in the above equation

\(\frac{2{\text{x}}}{2} \le \frac{8}{2}\)

x ≤ 4 

5 – 2x ≤ 3 

Subtracting 5 from both the sides in the above equation 

5 – 2x – 5 ≤ 3 – 5

-2x ≤ -2 

Now, multiplying by -1 on both the sides in the above equation 

-2x(-1) ≤ -2(-1) 

2x ≥ 2 

Now dividing by 2 on both the sides in the above equation

\(\frac{2{\text{x}}}{2} \ge \frac{2}{2}\)

x ≥ 1

Therefore,

x є [1, 4]