# Video: Writing and Solving Linear Equations

Jacqueline and Jane went jogging. Jane jogged 30 minutes longer than Jacqueline. If Jane jogged for 40 minutes, write an equation to determine how long Jacqueline jogged for, and then solve it.

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### Video Transcript

Jacqueline and Jane went jogging. Jane jogged for thirty minutes longer than Jacqueline. If Jane jogged for forty minutes, write an equation to determine how long Jacqueline jogged for, and then solve it. Okay, we’re trying to find out how long Jacqueline jogged for.

So let’s define a variable called 𝑥 which represents how long Jacqueline jogged for. Now in our question, the units for the length of time that people have jogging is minutes. So there’re the units that we’re gonna use for 𝑥. Now we can see that Jane jogged for forty minutes, and that was thirty minutes longer than Jacqueline jogged for.

Now this means that if we take the time that Jacqueline jogged, which we’ve called 𝑥, and we add thirty minutes to that, then we get the length of time that Jane jogged for, which was forty minutes.

Now it doesn’t matter whether we write 𝑥 plus thirty equals forty or thirty plus 𝑥 equals forty. They’re both equivalent and both perfectly good answers for the first part of the question. Now we’ve got to go on and solve that equation.

Well I want to know what 𝑥 is, so I’m gonna need to subtract thirty from the left-hand side of my equation so that I’ll be left with just 𝑥 on the left-hand side. Now I’ve unbalanced the equation, so also I need to subtract thirty from the right-hand side of the equation as well.

Now on the left-hand side, 𝑥 plus thirty minus thirty just leaves me with 𝑥; and on the right-hand side, forty minus thirty is ten. So we’ve got 𝑥 equals ten, but our answer to the actual question is that Jacqueline jogged for ten minutes.