Fill in each blank with an integer: (a) -5 - 4 = -5 + _ (b) -1 - (-6) = -1 + _

Understand the Problem

The question is asking to fill in the blanks with integers that would make the equations in parts (a) and (b) true. Essentially, we need to solve each equation step by step to find the correct integer.

Answer

For part (a): $-4$, for part (b): $6$.

Steps to Solve

Solve for the first equation (a)

Start with the equation: $$ -5 - 4 = -5 + x $$

Calculate the left side: $$ -5 - 4 = -9 $$

Now the equation updates to: $$ -9 = -5 + x $$

To isolate $x$, add 5 to both sides: $$ -9 + 5 = x $$

This simplifies to: $$ x = -4 $$

Solve for the second equation (b)

Start with the equation: $$ -1 - (-6) = -1 + y $$

Calculate the left side: $$ -1 - (-6) = -1 + 6 = 5 $$

Now the equation updates to: $$ 5 = -1 + y $$

To isolate $y$, add 1 to both sides: $$ 5 + 1 = y $$

This simplifies to: $$ y = 6 $$

For part (a), the blank is filled with $-4$.

For part (b), the blank is filled with $6$.

More Information

In part (a), we simplified the equation by solving for the unknown integer that makes both sides equal. In part (b), we evaluated the expression with the subtraction of a negative number, which results in addition.

Tips

Confusing subtraction of a negative number: Many may misinterpret $-(-6)$ as $-6$, while it should be evaluated as $+6$.
Not isolating the variable correctly: Ensure you perform the same operation on both sides of the equation to maintain equality.

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Fill in each blank with an integer: (a) -5 - 4 = -5 + ___ (b) -1 - (-6) = -1 + ___