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. 5 – 2x\| ≤ 3, x ϵ R.
Answer» 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]

Solve each of the following in equations and represent the solution set on the number line. 5 – 2x| ≤ 3, x ϵ R.

Answer»

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]