Which of the following is a linear equation in one variable?

• A. $2\left(x+5\right)-3x=x^2+1$
• B. $x\left(x+4\right)=0$
• C. $4\left(x+3\right)=2x+18$
• D. $x^2+5x=10$

Answer: (C)

Verified step by step guidance

1. Recall that a linear equation in one variable is an equation where the variable is only to the first power (exponent 1) and is not multiplied by itself or any other variable.
2. Examine each given equation and identify the highest power of the variable \(x\) in each:
3. For example, in the equation \$2\left(x+5\right)-3x = x^2 + 1\(, notice that \)x^2$ appears, which means the variable is squared, so this is not linear.
4. In the equation \(x\left(x+4\right) = 0\), when expanded, it becomes \(x^2 + 4x = 0\), which again has \(x^2\), so it is not linear.
5. Look at the equation \$4\left(x+3\right) = 2x + 18\(. When expanded, it becomes \)4x + 12 = 2x + 18\(, which only has \)x$ to the first power, so this is a linear equation in one variable.