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

$2 (x + 5) - 3 x = x^{2} + 1$

$x (x + 4) = 0$

$4 (x + 3) = 2 x + 18$

$x^{2} + 5 x = 10$

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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 another variable.

Examine each given equation and identify the highest power of the variable $x$ in each:

For the equation $2\left(x+5\right)-3x = x^2 + 1$, notice that $x^2$ (which is $x$ squared) appears, so this is not linear.

For the equation $x\left(x+4\right) = 0$, when expanded, it becomes $x^2 + 4x = 0$, which includes $x^2$, so it is not linear.

For 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.

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