Fill in each blank with an integer (signed number). (a) -2 _ = -2 + 5 (b) -1 - 2 = -1 + _
Understand the Problem
The question is asking to fill in the blanks with integers for two equations involving signed numbers. We need to calculate the missing values in both cases.
Answer
(a) $-5$, (b) $-2$
Answer for screen readers
The integers to fill in the blanks are:
(a) $-5$
(b) $-2$
Steps to Solve
- Solve equation (a)
Start with the equation:
$$ -2 - \square = -2 + 5 $$
First, simplify the right side:
$$ -2 + 5 = 3 $$
Now, the equation is:
$$ -2 - \square = 3 $$
Next, isolate $\square$:
$$ -\square = 3 + 2 $$
This simplifies to:
$$ -\square = 5 $$
Thus:
$$ \square = -5 $$
- Solve equation (b)
Start with the equation:
$$ -1 - 2 = -1 + \square $$
First, simplify the left side:
$$ -1 - 2 = -3 $$
Now the equation becomes:
$$ -3 = -1 + \square $$
Next, isolate $\square$:
$$ \square = -3 + 1 $$
This simplifies to:
$$ \square = -2 $$
The integers to fill in the blanks are:
(a) $-5$
(b) $-2$
More Information
In equation (a), we found that subtracting a negative results in a positive increase, while in equation (b), balancing the equation led to the solution of the second blank. This showcases how signed numbers can affect operations differently.
Tips
- Confusing the signs: Always remember that subtracting a negative number is equivalent to addition.
- Arithmetic errors: Double-check calculations when simplifying expressions or isolating variables.
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