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

Question

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

\(\frac{1}{2} \bigg(\frac{2}{3}x +1\bigg)\)\(\ge\) \(\frac{1}{3}\)\(\)(x - 2) Where x ϵ R

Answer 1

Given:

Now, subtracting \(\frac{1}{2}\) from both the sides in the above equation

Now, subtracting \(\frac{x}{3}\) from both the sides in the above equation,

\(0 \ge -\frac{7}{6}\)

Therefore, the solution is: true for all values of x