Solving equations using the additive inverse involves the concept of "undoing" addition or subtraction in an equation to isolate the variable. The additive inverse of a number is simply the number that, when added to the original number, results in zero. For example, the additive inverse of $5$ is $-5$, and the additive inverse of $-7$ is $7$.

Here’s a step-by-step guide:

Example Problem:

Solve the equation:
$x + 5 = 12$

Steps:

1. Identify the term that needs to be eliminated:
   The goal is to isolate $x$ by eliminating the $+5$.

2. Apply the additive inverse:
   The additive inverse of $+5$ is $-5$. Add $-5$ to both sides of the equation to cancel out the $+5$: $x + 5 - 5 = 12 - 5$

3. Simplify both sides:
   On the left side, $+5 - 5 = 0$, so: $x = 7$

4. Solution:
   The solution is $x = 7$.

Another Example:

Solve the equation:
$y - 8 = 3$

1. Identify the term that needs to be eliminated:
   The goal is to eliminate the $-8$.

2. Apply the additive inverse:
   The additive inverse of $-8$ is $+8$. Add $8$ to both sides: $y - 8 + 8 = 3 + 8$

3. Simplify both sides:
   $y = 11$

4. Solution:
   The solution is $y = 11$.

Key Idea:

To solve an equation using the additive inverse, always add or subtract the same amount on both sides of the equation to cancel out the term that involves the variable.

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Do you want more details or have any questions?

Here are 5 related questions:

1. How would you solve $z - 6 = 9$ using the additive inverse?
2. Can you solve an equation like $3x + 7 = 16$ using additive inverse first, then division?
3. How can the additive inverse be used in solving equations with decimals, like $x + 2.5 = 5.8$?
4. How do you apply the additive inverse to solve inequalities?
5. Can the additive inverse be used in solving systems of equations?

Tip: Always remember that whatever operation you apply to one side of the equation must also be applied to the other side to keep the equation balanced.