Question
Which one is not a linear equation? Choose the correct answer below. A. \( 0.03 x-0.07 x=0.30 \) B. \( 7 x+7 x=15 x \) (C. \( 2 x+7(x-1)=-3 x \) D. \( 8 x^{2}-3 x+3=0 \)
Ask by Schneider Vaughn. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**D. \( 8 x^{2} - 3 x + 3 = 0 \)** is not a linear equation.
Solution
The correct answer is:
**D. \( 8 x^{2} - 3 x + 3 = 0 \)**
**Explanation:**
A **linear equation** in one variable is an equation of the form \( ax + b = 0 \), where \( a \) and \( b \) are constants, and the highest power of \( x \) is 1.
Let's evaluate each option:
- **A. \( 0.03 x - 0.07 x = 0.30 \)**
- Simplifies to \( -0.04x = 0.30 \), which is linear.
- **B. \( 7 x + 7 x = 15 x \)**
- Simplifies to \( 14x = 15x \), which is linear.
- **C. \( 2 x + 7(x - 1) = -3 x \)**
- Expands to \( 2x + 7x - 7 = -3x \), which simplifies to \( 9x - 7 = -3x \), and further to \( 12x = 7 \). This is linear.
- **D. \( 8 x^{2} - 3 x + 3 = 0 \)**
- Contains \( x^2 \), making it a **quadratic equation**, not linear.
Therefore, **Option D** is **not** a linear equation.
**Answer:**
**D. \( 8 x^{2}-3 x+3=0 \)**
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Simplify this solution Bonus Knowledge
Let's take a fun look into why option D is the odd one out. The equation \( 8x^{2}-3x+3=0 \) is quadratic, as it has the term \( x^2 \). In contrast, the other options are linear equations because they each represent a straight line when graphed – just two variables and no powers higher than one in the equation! Now, if you're ever uncertain about identifying linear vs. non-linear equations, a great tip is to look for the highest power of the variable. If it’s one (or less), you’ve got a linear equation. If it's two or higher, well, welcome to the world of curves and bends! This simple rule can save you from mix-ups in the future!
