Fill in each blank with an integer. (a) -1 - _ = -1 + (-6) (b) -2 - (-3) = -2 + _

Understand the Problem

The question is asking us to fill in the blanks with integers for the arithmetic equations provided in (a) and (b). These equations involve subtraction and addition of integers. The goal is to find the appropriate integer values that satisfy the equations.

Answer

For (a): $6$; For (b): $3$

Steps to Solve

Solve Equation (a)

Start with the equation:

$$ -1 - x = -1 + (-6) $$

First, simplify the right side:

$$ -1 + (-6) = -7 $$

So, we have:

$$ -1 - x = -7 $$

Next, isolate $x$ by adding $1$ to both sides:

$$ -x = -7 + 1 $$

Which simplifies to:

$$ -x = -6 $$

Now, multiply both sides by $-1$:

$$ x = 6 $$

Solve Equation (b)

For the second equation:

$$ -2 - (-3) = -2 + y $$

Start by simplifying the left side:

$$ -2 - (-3) = -2 + 3 = 1 $$

So, we have:

$$ 1 = -2 + y $$

Next, isolate $y$ by adding $2$ to both sides:

$$ y = 1 + 2 $$

Which simplifies to:

$$ y = 3 $$

The values that satisfy the equations are:

For (a): $x = 6$
For (b): $y = 3$

More Information

In these equations, we used basic arithmetic operations and properties of numbers. Understanding how to manipulate integers and their signs is crucial in solving these types of equations.

Tips

Confusing the signs of numbers, like treating subtraction as addition.
Forgetting to simplify each side fully before trying to isolate the variable.
Miscalculating when adding or subtracting integers.

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Fill in each blank with an integer. (a) -1 - ___ = -1 + (-6) (b) -2 - (-3) = -2 + ___