One half a number increased by three is greater than zero or less than or equal to negative three
Answer:
The required inequality for both the statement is: \(\frac{1}{2} x+3>0\) and \(\frac{1}{2}x+3\leq -3\)
The solution for the inequalities are x>-6 and \(x\leq -12\) 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:
\(\frac{1}{2} x+3>0\)
Or One half a number increased by three is less than or equal to negative three.
Thus, the required inequality is:
\(\frac{1}{2}x+3\leq -3\)
Now solve the above inequality for x.
\(\frac{1}{2} x+3>0\) or \(\frac{1}{2}x+3\leq -3\)
\(\frac{1}{2} x>-3\) or \(\frac{1}{2}x\leq -3-3\)
\(x>-3\times 2\) or \(\frac{1}{2}x\leq -6\)
\(x>-6\) or \(x\leq -12\)
Hence, the value of x is \(x>-6\) or \(x\leq -12\)