# Solving Two-Step Linear Equations with Decimals

A two-step equation has two different operations. To solve a two-step equation, use inverse operations to undo each operation in reverse order.

Example :

Solve $4y+3.5=12.5$ . Check the solution.

Undo addition. Subtract $3.5$ from each side.

$4y+3.5-3.5=12.5-3.5$

Simplify.

$4y=9$

Undo multiplication. Divide each side by $4$ .

$\frac{4y}{4}=\frac{9}{4}$

Simplify.

$y=2.25$

To check the solution, substitute $2.25$ for $y$ in the equation.

$4\left(2.25\right)+3.5\stackrel{?}{=}12.25$

Simplify.

$\begin{array}{l}4\left(2.25\right)+3.5\stackrel{?}{=}12.25\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}9+3.5\stackrel{?}{=}12.25\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}12.5=12.5\end{array}$