Answer:
see explanation
Step-by-step explanation:
Given
x + [tex]\frac{1}{2}[/tex] ≤ - 3 or x - 3 > - 2
Solve the left and right inequalities separately, that is
x + [tex]\frac{1}{2}[/tex] ≤ - 3 ( isolate x by subtracting [tex]\frac{1}{2}[/tex] from both sides )
x ≤ - 3 - [tex]\frac{1}{2}[/tex], that is
x ≤ - [tex]\frac{6}{2}[/tex] - [tex]\frac{1}{2}[/tex], thus
x ≤ - [tex]\frac{7}{2}[/tex]
OR
x - 3 > - 2 ( isolate x by adding 3 to both sides )
x > 1
Solution is
x ≤ - [tex]\frac{7}{2}[/tex] or x > 1
