Solving One-Step Linear Equations: Multiplication

Some linear equations can be solved with a single operation. In these scenarios, we use the inverse operation to isolate the variable and solve for x. For example, we would use division to solve a multiplication problem because division is the inverse of multiplication.

In this article, we'll look at solving one-step linear equations involving multiplication. Let's get started!

Solving one-step linear equations: multiplication

The easiest way to do this is to look at a sample problem, so let's solve for x:

$5x=125$

This equation is telling us that 5 multiplied by x gives us 125, but we want to know what x equals. Therefore, we divide each side of the equation by 5 to isolate the variable:

$\frac{5x}{5}=\frac{125}{5}$

$x=25$

We're finished! Since we're dealing with one-step linear equations, each problem shouldn't take very long. That said, we still need to avoid rushing and double-check our work to make sure we come up with the correct answer.

Practice questions on solving one-step linear equations: multiplication

a. Solve for x:

$3x=15$

We need to isolate the variable, which means dividing each side by 3. When we do that, we get:

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

$x=5$

We can double-check our work by plugging our answer into the original equation and verifying we get the answer we're expecting. $3\times 5=15$ , so it checks out.

b. Solve for y:

$9y=72$

This problem uses y instead of x as the variable, but that doesn't change how we solve it. Isolating y requires dividing 9 from both sides of the equation, giving us:

$\frac{9y}{9}=\frac{72}{9}$

$y=8$

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Varsity Tutors can help with solving one-step linear equations: multiplication

Solving one-step linear equations with inverse operations is how students are introduced to algebra: a fundamental component of mathematics that students will be working with for the rest of their math careers. If your student is falling behind their peers or could use a helping hand to unlock their educational potential, a private tutor can provide personalized support to supplement the learning that happens in the classroom. Contact the friendly Educational Directors at Varsity Tutors for more info on the benefits of private instruction and how much it may cost.