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What is the reason for each step in the solution of the equation?

Given: [tex]\(12 - 5x + 6x = 4\)[/tex]

[tex]\[
\begin{array}{c|c}
\text{Step} & \text{Reason} \\
\hline
12 - 5x + 6x = 4 & \text{Given} \\
12 + x = 4 & \text{Combine like terms} \\
x = -8 & \text{Subtraction Property of Equality} \\
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(12 - 5x + 6x = 4\)[/tex] and explain the reason for each step:

1. Combine like terms:
- The original equation is [tex]\(12 - 5x + 6x = 4\)[/tex]. Start by combining like terms on the left-hand side. Since [tex]\(-5x\)[/tex] and [tex]\(+6x\)[/tex] are like terms, combine them to get [tex]\(12 + x = 4\)[/tex].
- Equation after this step: [tex]\(12 + x = 4\)[/tex].
- Reason: Combine like terms.

2. Subtraction Property of Equality:
- To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation. Subtract 12 from both sides of the equation: [tex]\(12 + x - 12 = 4 - 12\)[/tex].
- This simplifies to [tex]\(x = -8\)[/tex].
- Equation after this step: [tex]\(x = -8\)[/tex].
- Reason: Subtraction Property of Equality.

So, filling the reasons into the boxes:

- Step 1: [tex]\(12 - 5x + 6x = 4\)[/tex]
Reason: Given
- Step 2: [tex]\(12 + x = 4\)[/tex]
Reason: Combine like terms
- Step 3: [tex]\(x = -8\)[/tex]
Reason: Subtraction Property of Equality
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