Question
Solve the equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.
11xminus(5xplus4)plus14equals4x
11xminus(5xplus4)plus14equals4x
Answers
GPT-4o mini
To solve the equation \( 11x - (5x + 4) + 14 = 4x \), we'll first simplify the left side of the equation step by step.
1. Distribute the negative sign:
\[
11x - 5x - 4 + 14 = 4x
\]
2. Combine like terms:
\[
(11x - 5x) + (-4 + 14) = 4x
\]
\[
6x + 10 = 4x
\]
3. Now, isolate \( x \) by subtracting \( 4x \) from both sides:
\[
6x - 4x + 10 = 0
\]
\[
2x + 10 = 0
\]
4. Next, subtract 10 from both sides:
\[
2x = -10
\]
5. Finally, divide by 2:
\[
x = -5
\]
The solution to the equation is \( x = -5 \).
### Classification of the Equation:
Since we found a specific solution for \( x \) (i.e., \( x = -5 \)), the equation is classified as a **conditional equation** (an equation that is true for specific values of the variable).
In summary:
- Solution: \( x = -5 \)
- Type of equation: Conditional equation.
1. Distribute the negative sign:
\[
11x - 5x - 4 + 14 = 4x
\]
2. Combine like terms:
\[
(11x - 5x) + (-4 + 14) = 4x
\]
\[
6x + 10 = 4x
\]
3. Now, isolate \( x \) by subtracting \( 4x \) from both sides:
\[
6x - 4x + 10 = 0
\]
\[
2x + 10 = 0
\]
4. Next, subtract 10 from both sides:
\[
2x = -10
\]
5. Finally, divide by 2:
\[
x = -5
\]
The solution to the equation is \( x = -5 \).
### Classification of the Equation:
Since we found a specific solution for \( x \) (i.e., \( x = -5 \)), the equation is classified as a **conditional equation** (an equation that is true for specific values of the variable).
In summary:
- Solution: \( x = -5 \)
- Type of equation: Conditional equation.