Asked by find
Solve the equation justifying each step with the correct reasoning.
2 (x+8) = 2x + 8
give me the 2 steps and the 2 property's to get
for this equation there is/are ___________
2 (x+8) = 2x + 8
give me the 2 steps and the 2 property's to get
for this equation there is/are ___________
Answers
Answered by
GPT-4o mini
To solve the equation \( 2(x + 8) = 2x + 8 \), we will go through the following steps:
**Step 1:** Distribute the 2 on the left side.
\[
2(x + 8) = 2 \cdot x + 2 \cdot 8
\]
This simplifies to:
\[
2x + 16 = 2x + 8
\]
**Reasoning:** This step uses the **Distributive Property**, which states that \( a(b + c) = ab + ac \).
---
**Step 2:** Subtract \( 2x \) from both sides.
\[
2x + 16 - 2x = 2x + 8 - 2x
\]
This simplifies to:
\[
16 = 8
\]
**Reasoning:** This step uses the **Subtraction Property of Equality**, which states that if you subtract the same value from both sides of an equation, the equality is still maintained.
---
After performing these steps, we find that the resulting statement \( 16 = 8 \) is not true.
Thus, for this equation there are **no solutions** (it is inconsistent) since the simplified form leads to a false statement.
**Step 1:** Distribute the 2 on the left side.
\[
2(x + 8) = 2 \cdot x + 2 \cdot 8
\]
This simplifies to:
\[
2x + 16 = 2x + 8
\]
**Reasoning:** This step uses the **Distributive Property**, which states that \( a(b + c) = ab + ac \).
---
**Step 2:** Subtract \( 2x \) from both sides.
\[
2x + 16 - 2x = 2x + 8 - 2x
\]
This simplifies to:
\[
16 = 8
\]
**Reasoning:** This step uses the **Subtraction Property of Equality**, which states that if you subtract the same value from both sides of an equation, the equality is still maintained.
---
After performing these steps, we find that the resulting statement \( 16 = 8 \) is not true.
Thus, for this equation there are **no solutions** (it is inconsistent) since the simplified form leads to a false statement.
Answered by
GPT-4o mini
Sure! Here are the steps filled in as per your request:
**Step 1:** Distributing the \(2\) is the **Distributive Property** to get
\[
2x + 16 = 2x + 8.
\]
---
**Step 2:** Subtracting \(2x\) from both sides is the **Subtraction Property of Equality** to get
\[
16 = 8.
\]
---
This indicates that the equation has no solution, as \(16\) does not equal \(8\).
**Step 1:** Distributing the \(2\) is the **Distributive Property** to get
\[
2x + 16 = 2x + 8.
\]
---
**Step 2:** Subtracting \(2x\) from both sides is the **Subtraction Property of Equality** to get
\[
16 = 8.
\]
---
This indicates that the equation has no solution, as \(16\) does not equal \(8\).
Answered by
GPT-4o mini
No, the equation \(16 = 8\) is not a valid solution; instead, it is a false statement. The presence of \(16 = 8\) indicates that the original equation \(2(x + 8) = 2x + 8\) does not hold true for any value of \(x\).
In other words, when you simplify the equation, you end up with a contradiction, which shows that **there are no solutions** to the original equation.
To summarize:
- The equation simplifies to \(16 = 8\), which is false.
- Therefore, the original equation has **no solutions**.
In other words, when you simplify the equation, you end up with a contradiction, which shows that **there are no solutions** to the original equation.
To summarize:
- The equation simplifies to \(16 = 8\), which is false.
- Therefore, the original equation has **no solutions**.