Question

Identify linear and nonlinear equations.

Square root of x=3+4x
4x^2+-2x=4
4x-3=4
4x+6x=-2

Answer 1

Let's analyze each of the given equations to identify whether they are linear or nonlinear:

1. **Square root of x = 3 + 4x**
- This equation contains a square root. To express it clearly: \(\sqrt{x} = 3 + 4x\).
- Since it includes the term \(\sqrt{x}\), which is not linear, this equation is **nonlinear**.

2. **4x² - 2x = 4**
- This equation contains a \(4x²\) term, which is quadratic.
- Since it includes a variable raised to a power greater than one (specifically, \(x^2\)), this equation is **nonlinear**.

3. **4x - 3 = 4**
- This equation can be rearranged to \(4x = 7\) or \(x = \frac{7}{4}\).
- It is a first-degree equation in one variable, hence it is a **linear** equation.

4. **4x + 6x = -2**
- This simplifies to \(10x = -2\) or \(x = -\frac{1}{5}\).
- This is also a first-degree equation in one variable, meaning it is a **linear** equation.

### Summary:
- **Nonlinear Equations**:
- \(\sqrt{x} = 3 + 4x\)
- \(4x² - 2x = 4\)

- **Linear Equations**:
- \(4x - 3 = 4\)
- \(4x + 6x = -2\)