Question Video: Rearranging and Solving Linear Equations Mathematics • 8th Grade

Solve 4𝑥 − 3 = 11 − 3𝑥.

03:29

Video Transcript

Solve four 𝑥 minus three equals eleven minus three 𝑥. Well I’m gonna use inverse operations either to eliminate four 𝑥 from this side by subtracting four 𝑥 from both sides or eliminating negative three 𝑥 from this side by adding three 𝑥 to both sides. So I just need to think carefully which one am I gonna do. If I subtract four 𝑥 from both sides, yes I will eliminate four 𝑥 from the left-hand side; but on the right hand side, I’m gonna have negative three 𝑥 take away another four 𝑥. I’m gonna leave myself with negative seven 𝑥, so I’m not gonna do that. If I add three 𝑥 to both sides, that will eliminate negative three 𝑥 on the right-hand side. But on the left-hand side, I’m gonna have four 𝑥 plus three 𝑥, which will leave me with positive seven 𝑥. So this is the inverse operation that I’m gonna do to both sides. So I’ve got my original equation, but I’m adding three 𝑥 to both sides. And four 𝑥 plus three 𝑥 is seven 𝑥. And then I’ve got to subtract three, so still got this term here. On the right-hand side, I’ve got negative three 𝑥 add three 𝑥. Well that becomes zero, so they cancel out. So I’ve just got eleven. Now on the left-hand side, I’ve got seven 𝑥 take away three. So the inverse operation of taking away three is adding three. So I’m gonna add three to both sides of the equation. So on the left-hand side, I had my seven 𝑥 minus three and I’m adding three to that. And on the right-hand side, I had eleven and I’m adding three to that. Now over on the left-hand side, negative three add three is nothing. That was the whole point of adding three to both sides, so I’m just left with seven 𝑥. And on the right-hand side, eleven plus three is fourteen. For now I’ve got seven 𝑥 is equal to fourteen. Well this means seven times 𝑥. And the inverse operation to times-ing by seven is dividing by seven. So I’m going to divide both sides of my equation by seven. And that means on the left-hand side, I’ve got seven on the top and seven on the bottom. So divide seven by seven, I get one. Divide seven by seven, I get one. So I’ve just got 𝑥 on the left-hand side. And fourteen divided by seven is just two on the right-hand side, so my answer is 𝑥 equals two. Now I’m just gonna check my answer as well just to make sure that’s right. So on the left-hand side of my original equation, it said four 𝑥 minus three. Well we now know that 𝑥 is equal to two. So we’re gonna replace the 𝑥 with two. So that becomes four times two minus three. And four times two is eight, so eight minus three and eight minus three is equal to five. So the left-hand side is equal to five. So let’s see what the right-hand side would be when we substitute 𝑥 equals two into that. Well eleven minus three 𝑥, if 𝑥 is two, that is the same as eleven minus three times two. And three times two is six. So eleven minus six is equal to five. And that is the same as the left-hand side, so they are equal. So it looks like we were right. So if you’re doing these sorts of questions in a test or in an exam, then if you’ve got a bit of time left at the end, always do the check cause then you know whether you got the right answer or not. If you did make a slip somewhere and write the wrong number down, at least you’ve got time to correct that.

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