Question

Solve and graph on a number line.

A. x - 1/6 ≥ 2/3 

B. -4x ≥ 24

Answer 1

• A).

The inequality is x - 1/6 ≥ 2/3.

Apply addition property of inequality : .

x - 1/6 + 1/6 ≥ 2/3 + 1/6

x  ≥ 2/3 + 1/6

Take Least Common Multiple of 3 and 6 i.e., 6.

x  ≥ (2*2 + 1) / 6

x  ≥ (4 + 1) / 6

x  ≥ 5 / 6

The solution set is {x | x  ≥ 5 / 6}.

Graph the solution set on a number line :

A dot means that this point is included in the solution set.

• (B).

The inequality is - 4x ≥ 24.

Apply division property of inequality : If a ≥ b, then a /c ≤ b /c where c < 0 (c is negative).

Divide each side by negative 4 and reverse the inequality symbol.

(- 4x ) / (- 4) ≤ (6*4) / (- 4)

Cancel common terms.

x ≤ - 6.

The solution set is {x | x ≤ - 6}.

Graph the solution set on a number line :

A dot means that this point is included in the solution set.