Solve five 𝑥 minus two equals two
𝑥 plus 19.
So to solve this equation, we want
to work out the value of 𝑥. And what we notice first of all is
that 𝑥 currently appears on both sides of the equation. We want to collect all of the 𝑥
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 𝑥 terms
on the side that initially has the larger number of 𝑥s. So in this case, that’s the
left-hand side of the equation.
So we want to eliminate the 𝑥
terms on the right of the equation. And at the moment, we have two 𝑥
there. So to cancel this out, we need to
substract two 𝑥. 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 𝑥
from the left side of the equation.
So when we subtract two 𝑥 from the
right side of this equation, this cancels out with the two 𝑥 that was there and
just leaves 19. On the left of the equation, we
have five 𝑥 minus two 𝑥 which is equal to three 𝑥. And we still have that negative
two. So the equation simplifies to three
𝑥 minus two is equal to 19.
Now, remember we’re trying to solve
for 𝑥, which means we want to just be left with one 𝑥 or 𝑥 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
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
𝑥. And on the right, we have 19 plus
two which is equal to 21. So now, our equation has become
three 𝑥 is equal to 21. And we’re nearly there with solving
Now, remember that three 𝑥 means
three times 𝑥. So we know that three times 𝑥 is
equal to 21. To work out what just one lot of 𝑥
is equal to, we need to divide by three. But again, we need to do this to
both sides of the equation. Dividing three 𝑥 by three gives
one 𝑥, which remember we just write it as 𝑥. And dividing 21 by three gives
seven because that’s one of our times tables. Three multiplied by seven is equal
So now, we have 𝑥 is equal to
seven. And we’ve solved the equation. The solution to the equation five
𝑥 minus two equals two 𝑥 plus 19 is 𝑥 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 𝑥 that we found into both sides of the equation.
On the left of the equation, we
have the expression five 𝑥 minus two. So substituting 𝑥 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 𝑥 plus 19. So substituting 𝑥 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 𝑥 equals
seven is substituted in. So the left-hand side is equal to
the right-hand side. And this confirms that our solution
of 𝑥 equals seven is correct.