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# 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 $5×3+8=23$ , 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.

$11.25+4.5=15.75$

$15.75=15.75$

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.

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

$3x=18$

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.

## Flashcards covering the Solving Two-Step Linear Equations with Decimals

Algebra 1 Flashcards