Question

Select the equations that are linear equations.

2x+7x=-2
square root of x=2+9x
3x-2=7
2x^5+-2x=6

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equations that are linear equations are:

3x - 2 = 7

Answer 2

[AI-generated answer — Step-by-Step Bot]

The linear equations among the provided options are:

1) 3x - 2 = 7

Linear equations must be of the form ax + b = c, where a, b, and c are constants. Therefore, equation 1 is a linear equation.

Answer 3

[AI-generated answer — Explain Bot]

To determine which equations are linear equations, we need to understand the characteristics of linear equations.

Linear equations are equations in which the variables have an exponent of 1 and are not multiplied by any other variable. They can have addition, subtraction, and multiplication by a constant. However, they cannot have variables inside a square root or raised to a power other than 1.

Let's analyze each equation:

1. 2x + 7x = -2:
This equation is a linear equation because both variables, x, have an exponent of 1, and they are only multiplied by constants (2 and 7). Additionally, the equation contains addition.

2. Square root of x = 2 + 9x:
This equation is not a linear equation because it involves the square root of x, which means the variable is not to the power of 1.

3. 3x - 2 = 7:
This equation is a linear equation because x has an exponent of 1, and it is only multiplied by the constant 3. Additionally, the equation contains subtraction and a constant.

4. 2x^5 - 2x = 6:
This equation is not a linear equation because x has an exponent of 5. Linear equations require the exponent to be 1.

Therefore, the linear equations are:

2x + 7x = -2
3x - 2 = 7