# Solving Two-Step Linear Equations

While you can sometimes solve linear equations in a single step, it's more common to need two or more separate steps to solve for x. For example, the equation $3x+5=11$ calls for the value of x to be multiplied by 3 and then increased by 5. Solving this equation entails using inverse operations to undo each operation in reverse order, ultimately trying to isolate the x on one side of the equals sign.

Starting with $3x+5=11$ , the first step is subtracting 5 from each side:

$3x=6$

Next, we want to divide each side by 3 to get x by itself:

$x=2$

We've solved the equation. As long as you remember to use the appropriate inverse operations (addition to undo subtraction, subtraction to undo addition, multiplication to undo division, and division to undo multiplication), and add/subtract before you multiply/divide, these problems can be pretty fun!

## Why is this solving two-step “linear” equations?

Equations like the one above are considered "linear" because ${x}^{1}$ is the highest exponent present: there are no ${x}^{2}$ , ${x}^{3}$ , or any other powers. If you want to learn how to work with equations involving exponents, you'll want quadratic equations and polynomials.

Linear equations can also have more than one variable. For example, consider $y=3x+2$ . You cannot solve an equation like this the way we did above because there are an infinite number of solutions based on different values for x and y. However, you can graph the equation as a line on the plane. Setting y to 0 and solving for x will reveal the coordinates of the y-intercept and help you graph it. Likewise, setting x to 0 and solving for y gives you the x-intercept. These are not the only solutions to the equation, but they will give you the two points you need to sketch the line.

## Solving two-step linear equations practice questions

a. $5x+5=30$

To solve for x, first subtract 5 from both sides:

$5x=25$

Now, divide both sides by 5:

$x=5$

b. $7x-1=27$

To solve for x, first add 1 to both sides:

$7x=28$

Now, divide both sides by 7:

$x=4$

c. $\frac{x}{4}+2=18$

To solve for x, first subtract 2 from both sides:

$\frac{x}{4}=16$

Now, multiply both sides by 4:

$x=64$

d. $\frac{x}{3}-7=8$

To solve for x, first add 7 to both sides:

$\frac{x}{3}=15$

Now, multiply both sides by 3:

$x=45$

## Topics related to the Solving Two-Step Linear Equations

Solving Systems of Linear Equations

Writing Systems of Linear Equations from Word Problems

Describing the Graph of a Function

## Flashcards covering the Solving Two-Step Linear Equations

## Practice tests covering the Solving Two-Step Linear Equations

College Algebra Diagnostic Tests

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Two-step linear equations introduce students to working with functions, a vital skill that they will hone throughout their high school years and beyond. If your student appears to be struggling, they may not have the foundational skills they need to effectively study more advanced concepts in mathematics. Luckily, an experienced math tutor can introduce topics like two-step linear equations in fresh ways and within a learning environment ideally suited to your student's needs. Reach out to the knowledgeable Educational Directors at Varsity Tutors today for more information on the benefits of 1-on-1 tutoring and to sign up today!

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