Solving Two-Step Linear Equations with Decimals

An equation is a number statement that includes an equal sign, such as $5x+8=23$ . A linear equation is an equation where the variable or variables are either added to or multiplied by numbers with nothing more complicated than that. There are no exponents, no square roots, no rational expressions like 1/x, or any other more complex calculations.

A solution to a linear equation is a number that can be plugged in for the variable to make a true number statement. For example, in the above equation, $5x+8=23$ , if you plug in 3 for x, you get $5\times 3+8=23$ , which is a true statement. This is also a two-step linear equation because you have to complete two steps, multiplication and addition.

Using inverse operations to solve two-step linear equations with decimals

To solve a two-step linear equation, with or without decimals, you use inverse operations to undo the math in the reverse of the order of operations.

Example 1

Solve $5x+4.5=15.75$ . Then check the solution.

We're going to undo the math in the reverse of the order of operations, so we will undo the addition first.

$5x+4.5-4.5=15.75-4.5$

Simplify by performing the subtraction.

$5x=11.25$

Next, we will undo the multiplication by dividing each side by 5.

$\frac{5x}{5}=\frac{11.25}{5}$

Simplify by performing the division.

$x=2.25$

To check the solution, substitute 2.25 for x in the equation.

$5\left(2.25\right)+4.5=15.75$

Now we're using the order of operations in the correct order, so first, perform the multiplication.

$11.25+4.5=15.75$

Then perform the addition.

$15.75=15.75$

We have solved the problem correctly.

Example 2

Solve $3x-7.8=10.2$ . Then check the solution.

We're going to undo the math in the reverse of the order of operations, so we will undo the subtraction first.

$3x-7.8+7.8=10.2+7.8$

Simplify by performing the addition.

$3x=18$

Next, we will undo the multiplication by dividing each side by 3.

$\frac{3x}{3}=\frac{18}{3}$

Simplify by performing the division.

$x=6$

To check the solution, substitute 6 for x in the equation.

$3\left(6\right)-7.8=10.2$

Now we're using the order of operations in the correct order, so first, perform the multiplication.

$18-7.8=10.2$

Then perform the subtraction.

$10.2=10.2$

We have solved the problem correctly.

Topics related to the Solving Two-Step Linear Equations with Decimals

Solving Systems of Linear Equations

Reduced Radical Form

Term of a Sequence

Flashcards covering the Solving Two-Step Linear Equations with Decimals

Algebra 1 Flashcards

College Algebra Flashcards

Practice tests covering the Solving Two-Step Linear Equations with Decimals

Algebra 1 Diagnostic Tests

College Algebra Diagnostic Tests

Get help learning about two-step linear equations with decimals

Tutoring is a great way for your student to supplement their in-class learning about two-step linear equations with decimals. Being able to solve linear equations is an essential skill for any student, and if your student is having trouble with linear equations with decimals, meeting with a tutor is a great way to bring them up to speed. A tutor can provide your student with constant, in-the-moment feedback so they solve the two-step linear equations with decimals the correct way from the beginning and don't let bad habits take root. If you'd like to find out more about how tutoring can help your student, contact Varsity Tutors and speak with one of our Educational Directors. We'd be happy to connect you with a qualified tutor to help your student understand two-step linear equations with decimals.