Fill in each blank with an integer (signed number). (a) 2 - 7 = 2 + __ (b) 5 - (-1) = 5 + __
Understand the Problem
The question is asking to fill in the blanks in two mathematical equations with integers, specifically signed numbers. We need to evaluate and solve the left side of each equation to determine the correct signed number to fill in each blank.
Answer
(a) \(-7\), (b) \(1\)
Answer for screen readers
(a) (-7), (b) (1)
Steps to Solve
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Evaluate the first equation: (2 - 7 = 2 + ______ )
Start by simplifying the left side of the equation.
Calculate (2 - 7): $$ 2 - 7 = -5 $$
Now, rewrite the equation: $$ -5 = 2 + ______ $$
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Isolate the blank in the first equation
Subtract (2) from both sides to find the integer needed for the blank: $$ -5 - 2 = ______ $$ $$ -7 = ______ $$
Therefore, the blank for part (a) is (-7).
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Evaluate the second equation: (5 - (-1) = 5 + ______ )
Next, simplify the left side of the equation. Remember that subtracting a negative is the same as adding a positive.
Calculate (5 - (-1)): $$ 5 - (-1) = 5 + 1 = 6 $$
Now, rewrite the equation: $$ 6 = 5 + ______ $$
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Isolate the blank in the second equation
Subtract (5) from both sides to find the integer needed for the blank: $$ 6 - 5 = ______ $$ $$ 1 = ______ $$
Therefore, the blank for part (b) is (1).
(a) (-7), (b) (1)
More Information
The first equation illustrates how to handle subtraction with signed numbers. In part (b), it demonstrates how subtracting a negative number effectively results in addition.
Tips
- Confusing subtraction with negative numbers; remember that subtracting a negative is equivalent to adding the absolute value.
- Not simplifying expressions correctly before isolating the blank.
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