Video: GCSE Mathematics Foundation Tier Pack 4 β€’ Paper 1 β€’ Question 27

GCSE Mathematics Foundation Tier Pack 4 β€’ Paper 1 β€’ Question 27

03:57

Video Transcript

Solve five π‘₯ minus two equals two π‘₯ plus 19.

So to solve this equation, we want to work out the value of π‘₯. And what we notice first of all is that π‘₯ currently appears on both sides of the equation. We want to collect all of the π‘₯ terms on the same side of the equation. And because it’s easier to work with positive rather than negative numbers, we want to collect all of the π‘₯ terms on the side that initially has the larger number of π‘₯s. So in this case, that’s the left-hand side of the equation.

So we want to eliminate the π‘₯ terms on the right of the equation. And at the moment, we have two π‘₯ there. So to cancel this out, we need to substract two π‘₯. However, when we’re solving an equation, whatever we do to one side of the equation, we must make sure we also do to the other. So we also need to subtract two π‘₯ from the left side of the equation.

So when we subtract two π‘₯ from the right side of this equation, this cancels out with the two π‘₯ that was there and just leaves 19. On the left of the equation, we have five π‘₯ minus two π‘₯ which is equal to three π‘₯. And we still have that negative two. So the equation simplifies to three π‘₯ minus two is equal to 19.

Now, remember we’re trying to solve for π‘₯, which means we want to just be left with one π‘₯ or π‘₯ on the left of this equation. So next, we notice that there’s a negative two. In order to eliminate this negative two, we need to add two to the left of the equation as negative two plus two just gives zero.

But we need to do the same thing to both sides. So we also need to add two to the right of the equation. So when we add this two, it cancels out the negative two on the left. And we’re just left with three π‘₯. And on the right, we have 19 plus two which is equal to 21. So now, our equation has become three π‘₯ is equal to 21. And we’re nearly there with solving for π‘₯.

Now, remember that three π‘₯ means three times π‘₯. So we know that three times π‘₯ is equal to 21. To work out what just one lot of π‘₯ is equal to, we need to divide by three. But again, we need to do this to both sides of the equation. Dividing three π‘₯ by three gives one π‘₯, which remember we just write it as π‘₯. And dividing 21 by three gives seven because that’s one of our times tables. Three multiplied by seven is equal to 21.

So now, we have π‘₯ is equal to seven. And we’ve solved the equation. The solution to the equation five π‘₯ minus two equals two π‘₯ plus 19 is π‘₯ equals seven.

Now, it’s always sensible to check our answers where we can. So what we’re going to do is substitute this value of π‘₯ that we found into both sides of the equation.

On the left of the equation, we have the expression five π‘₯ minus two. So substituting π‘₯ equals seven, this is equal to five multiplied by seven minus two. Five multiplied by seven is 35 and 35 minus two is 33. So the left side of the equation is equal to 33.

On the right of the equation, we have the expression two π‘₯ plus 19. So substituting π‘₯ equals seven, this gives two multiplied by seven plus 19. Two multiplied by seven is equal to 14 and 14 plus 19 is equal to 33.

Now, notice that both the left-hand side and the right-hand side of this equation give a value of 33 when π‘₯ equals seven is substituted in. So the left-hand side is equal to the right-hand side. And this confirms that our solution of π‘₯ equals seven is correct.

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