Fill in each blank with an integer (signed number). (a) 5 - (-3) = __ + 3 (b) 2 - 6 = 2 + __
Understand the Problem
The question is asking us to fill in the blanks with appropriate integers that satisfy the given equations for parts (a) and (b). We need to solve the equations to find the correct integers.
Answer
(a) \( 5 \) (b) \( 6 \)
Answer for screen readers
(a) ( 5 )
(b) ( 6 )
Steps to Solve
- Solve Equation for (a)
We start with the equation:
$$ 5 - (-3) = _ + 3 $$
First, simplify the left side:
$$ 5 + 3 = _ + 3 $$
Now, add the left side:
$$ 8 = _ + 3 $$
Next, isolate the blank:
$$ _ = 8 - 3 $$
- Calculate the value for (a)
Now solve for the blank:
$$ _ = 5 $$
This means that in part (a), we fill in the blank with $5$.
- Solve Equation for (b)
Now we move to part (b):
$$ 2 - 6 + _ = 2 $$
First, simplify the left side:
$$ -4 + _ = 2 $$
Isolate the blank:
$$ _ = 2 + 4 $$
- Calculate the value for (b)
Now solve for the blank:
$$ _ = 6 $$
This means that in part (b), we fill in the blank with $6$.
(a) ( 5 )
(b) ( 6 )
More Information
In part (a), we simplified the expression to find that adding 5 to 3 results in 8. In part (b), we needed to make the expression equal to 2 by finding that we needed to add 6.
Tips
- Confusing subtraction with negative numbers: Remember that subtracting a negative is equivalent to addition.
- Not isolating the blank correctly: Always perform operations to both sides of the equation to maintain balance.
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