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

$2\left(x+5\right)-3x=x^2+1$

$x\left(x+4\right)=0$

$4\left(x+3\right)=2x+18$

$x^2+5x=10$

Verified step by step guidance

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 inside any other function (like squares, square roots, etc.).

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 the term $x^2$ on the right side, which means this is not linear because the variable is squared.

For 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.

For the equation \$4\left(x+3\right) = 2x + 18$, expand the left side to get $4x + 12 = 2x + 18$. Here, the variable $x$ is only to the first power and appears linearly, so this is a linear equation in one variable.

6:06m

Watch next

Master Introduction to Linear Equations with a bite sized video explanation from Patrick Ford