8.1 Solve equations using the subtraction and addition properties

We are now ready to “get to the good stuff.” You have the basics down and are ready to begin one of the most important topics in algebra: solving equations. The applications are limitless and extend to all careers and fields. Also, the skills and techniques you learn here will help improve your critical thinking and problem-solving skills. This is a great benefit of studying mathematics and will be useful in your life in ways you may not see right now.

Solve equations using the subtraction and addition properties of equality

We began our work solving equations in previous chapters. It has been a while since we have seen an equation    , so we will review some of the key concepts before we go any further.

We said that solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.

In the earlier sections, we listed the steps to determine if a value is a solution. We restate them here.

Determine whether $y=\frac{3}{4}$ is a solution for $4y+3=8y.$

Solution

Multiply.
Add.

Since $y=\frac{3}{4}$ results in a true equation, $\frac{3}{4}$ is a solution to the equation $4y+3=8y.$

Got questions? Get instant answers now!

Got questions? Get instant answers now!

We introduced the Subtraction and Addition Properties of Equality in Solving Equations Using the Subtraction and Addition Properties of Equality . In that section, we modeled how these properties work and then applied them to solving equations with whole numbers. We used these properties again each time we introduced a new system of numbers. Let’s review those properties here.