Fill in each blank with an integer (signed number). (a) 2 - (-3) = 2 + __ (b) 3 - 5 = 3 + __
Understand the Problem
The question is asking to fill in the blanks with signed integers that correctly complete the equations provided. This involves solving basic algebraic expressions with integers.
Answer
(a) $3$, (b) $-5$
Answer for screen readers
(a) The blank is filled with $3$.
(b) The blank is filled with $-5$.
Steps to Solve
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Calculate the left side of equation (a)
For the expression $2 - (-3)$, we need to change the subtraction of a negative into addition: $$ 2 - (-3) = 2 + 3 = 5 $$
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Set equation (a) equal and solve for the blank
Now, equate this to the right side of the equation: $$ 5 = 2 + \text{blank} $$
To find the blank, rearrange the equation: $$ \text{blank} = 5 - 2 = 3 $$
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Calculate the left side of equation (b)
For the expression $3 - 5$, compute: $$ 3 - 5 = -2 $$
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Set equation (b) equal and solve for the blank
Now, equate this to the right side of the equation: $$ -2 = 3 + \text{blank} $$
To find the blank, rearrange: $$ \text{blank} = -2 - 3 = -5 $$
(a) The blank is filled with $3$.
(b) The blank is filled with $-5$.
More Information
In algebra, subtracting a negative number is equivalent to adding its positive counterpart. This helps simplify expressions efficiently.
Tips
- Overlooking signs: Make sure to correctly apply the rules of signs, particularly when subtracting negative numbers.
- Mistakes in basic arithmetic: Double-check calculations, especially when adding or subtracting integers.
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