Solve each of the following in equations and represent the solution set on the number line. (2x- 1)(3)≥ (3x - 2)/5-(2-x)/5

Question

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

\(\frac{\big(2{\text{x}}-1\big)}{3}\)\(\ge\) \(\frac{\big(3{\text{x}}-2\big)}{4}\) - \(\frac{\big(2-{\text{x}}\big)}{5}\)

Answer 1

 \(\frac{\big(2{\text{x}}-1\big)}{3}\)\(\ge\) \(\frac{\big(3{\text{x}}-2\big)}{4}\) - \(\frac{\big(2-{\text{x}}\big)}{5}\), where x ϵ R.

Multiplying by 60 on both the sides in the above equation.

 \((60)\frac{\big(2{\text{x}}-1\big)}{3}\)\(\ge\) \((60)\frac{\big(3{\text{x}}-2\big)}{4}\) - (60)\(\frac{\big(2-{\text{x}}\big)}{5}\)

20(2x – 1) ≥ 15(3x – 2) -12(2 – x) 

40x – 20 ≥ 45x – 30 – 24 + 12x 

40x – 20 ≥ 57x – 54 

Now, Adding 20 on both the sides in the above equation 

40x – 20 + 20 ≥ 57x – 54 + 20 

40x ≥ 57x – 34 

Now, subtracting 57x from both the sides in the above equation

40x – 57x ≥ 57x – 34 – 57x 

-17x ≥ -34 

Multiplying by -1 on both sides in the above equation 

(-17x)(-1) ≥ (-34)(-1) 

17x ≤ 34 

Now, divide by 17 on both sides in the above equation

\(\frac{17{\text{x}}}{17}\)\(\le\) \(\frac{34}{17}\)

Therefore, 

x ≤ 2