What should be added to -12 + (-98) - (-84) + (-7) to make 30?

Options

A. `-63`
B. `63`
C. `-33`
D. `33`

Answer

To solve the problem step by step, we need to determine what should be added to the expression \(-12 + (-98) - (-84) + (-7)\) to make it equal to 30.

### Step 1: Simplify the Expression
We start with the expression:
\[ -12 + (-98) - (-84) + (-7) \]
This can be rewritten as:
\[ -12 - 98 + 84 - 7 \]

### Step 2: Combine the Negative Numbers
Now, we combine the negative numbers:
\[ -12 - 98 - 7 \]
Calculating this step by step:
- First, add \(-12\) and \(-98\):
\[ -12 - 98 = -110 \]
- Now, add \(-110\) and \(-7\):
\[ -110 - 7 = -117 \]
So, we have:
\[ -12 - 98 - 7 = -117 \]

### Step 3: Add the Positive Number
Next, we add \(84\) to \(-117\):
\[ -117 + 84 \]
Since \(117\) is greater than \(84\), we will subtract:
\[ 117 - 84 = 33 \]
The sign will be negative because \(-117\) has a greater absolute value:
\[ -117 + 84 = -33 \]

### Step 4: Set Up the Equation
Now, we need to find out what should be added to \(-33\) to make it \(30\). Let that number be \(x\):
\[ -33 + x = 30 \]

### Step 5: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = 30 + 33 \]
Calculating this gives:
\[ x = 63 \]

### Conclusion
Thus, the number that should be added to \(-12 + (-98) - (-84) + (-7)\) to make it \(30\) is:
\[ \boxed{63} \]