Question

Which of the following is/are multi step equations?

• A. $x-3=0$
• B. $6x-18=0$
• C. $x+3=\frac{x}{2}-1$
• D. $5x+7=x-1$

Answer 1

Answer: (C), (D)

$5x+7=x-1$

To solve multi-step equations, you need to solve more than two mathematical operations to find the solution of an equation.

$\left(A\right)x-3=0$
Add 3 to both the sides
$x-3+3=0+3\Rightarrow x=3$
$\therefore$ It took only one step to solve the equation. So, it is an one step equation.

$\left(B\right)6x-18=0$
Add 18 to both the sides
$6x-18+18=0+18$
$\Rightarrow 6x=18$
Divide both the sides by $6$
$\frac{6x}{6}=\frac{18}{6}$
$\Rightarrow x=3$
$\therefore$ It took two steps to solve the equation. So, it is a two step equation.

$\left(C\right)x+3=\frac{x}{2}-1$
Subtract both the sides by $\frac{x}{2}$
$x+3-\frac{x}{2}=\frac{x}{2}-1-\frac{x}{2}$
$\frac{x}{2}+3=-1$
Subtract both the sides by $3$
$\frac{x}{2}+3-3=-1-3$
$\Rightarrow \frac{x}{2}=-4$
Multiply both the sides by $2$
$\frac{x}{2}\times 2=-4\times 2$
$\Rightarrow x=-8$
$\therefore$ It took three steps to solve the equation. So, it is a multi step equation.

$\left(D\right)5x+7=x-1$
Subtract both the sides by $x$
$5x+7-x=x-1-x$
$\Rightarrow 4x+7=-1$
Subtract both the sides by $7$
$4x+7-7=-1-7$
$\Rightarrow 4x=-8$
Divide both the sides by $4$
$\frac{4x}{4}=\frac{-8}{4}$
$\Rightarrow x=-2$
$\therefore$ It took three steps to solve the equation. So, it is a multi step equation.