Respuesta :
Answer:
The required inequality for both the statement is: [tex]\frac{1}{2} x+3>0[/tex] and [tex]\frac{1}{2}x+3\leq -3[/tex]
The solution for the inequalities are x>-6 and [tex]x\leq -12[/tex] respectively.
Step-by-step explanation:
Consider the provided information.
One half a number increased by three is greater than zero
Let the number is x.
Thus, the required inequality is:
[tex]\frac{1}{2} x+3>0[/tex]
Or One half a number increased by three is less than or equal to negative three.
Thus, the required inequality is:
[tex]\frac{1}{2}x+3\leq -3[/tex]
Now solve the above inequality for x.
[tex]\frac{1}{2} x+3>0[/tex] or [tex]\frac{1}{2}x+3\leq -3[/tex]
[tex]\frac{1}{2} x>-3[/tex] or [tex]\frac{1}{2}x\leq -3-3[/tex]
[tex]x>-3\times 2[/tex] or [tex]\frac{1}{2}x\leq -6[/tex]
[tex]x>-6[/tex] or [tex]x\leq -12[/tex]
Hence, the value of x is [tex]x>-6[/tex] or [tex]x\leq -12[/tex]
