Question
Which one is not a linear equation? Choose the correct answer below. A. \( 0.03 x-0.08 x=0.30 \) B. \( 5 x+4(x-1)=-2 x \) C. \( 8 x^{2}-3 x+2=0 \) D. \( 4 x+8 x=11 x \)
Ask by Barrett Carter. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Option C is not a linear equation.
Solution
To determine which equation is **not** a linear equation, let's analyze each option:
**A. \( 0.03x - 0.08x = 0.30 \)**
- Simplify: \(-0.05x = 0.30\)
- This is a linear equation since it can be written in the form \(ax + b = 0\).
**B. \( 5x + 4(x - 1) = -2x \)**
- Expand and simplify: \(5x + 4x - 4 = -2x\) → \(9x - 4 = -2x\) → \(11x = 4\)
- This is a linear equation as it reduces to \(x = \frac{4}{11}\).
**C. \( 8x^{2} - 3x + 2 = 0 \)**
- This equation includes an \(x^2\) term, making it a quadratic equation.
- **Not a linear equation** because it has a degree of 2.
**D. \( 4x + 8x = 11x \)**
- Simplify: \(12x = 11x\) → \(x = 0\)
- This is a linear equation since it resolves to a single solution for \(x\).
**Conclusion:**
**Option C** is the equation that is **not** linear.
**Answer:**
C. \( 8 x^{2}-3 x+2=0 \)
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Simplify this solution Extra Insights
The equation that is not a linear equation is C. \( 8 x^{2}-3 x+2=0 \). This is a quadratic equation because it contains a term with \( x^2 \), which makes it a polynomial of degree 2. Linear equations, on the other hand, only involve terms to the first power of \( x \). When identifying linear equations, remember that they can be expressed in the form \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) is the variable. Common mistakes involve overlooking the degree of terms, so always check for the highest exponent present!
