Math Is Fun Forum

Ok. A bit of gear crunching but we're getting there.

Q2. Completely correct.

Q3. Correct on imgur.  When you type it as text you need to surround y-c with a bracket to make it clear that the subtract takes precedence over the divide.  The way you've written it is correct on imgur.  As text it needs to be x = (y-c)/m

Q1 It was supposed to be 'a' the subject, not t. But also the same issue here.  We want to force the subtraction first otherwise the PEDMAS rules (or do you say BODMAS?) would give the division precedence and your answer would be

rather than

If you try some numbers in the original to fix 'v' and then put v,u and t into each of the above you'll soon see which gives the correct a.

OK. Let's move onto step 3.  It wasn't needed in any so far but it is in the next example.

eg. y + x = z + bx   Make x the subject.

In this one there are two terms with x in them.  If you just tried to get one of the x on its own and equal to something with everything else, then x would depend on an expression with x in.  That's no use if we want a formula for calculating x.

x = z + bx - y is a correct formula but you cannot work out x from it as bx is part of the right hand side.

So we need a way to obtain a single x in the equation.

Step 2 says get all the x containing terms on the left.  Up until now there was only one but now there's two.

Subtract y from both sides and subtract bx from both sides

Step 3: Factorise the x out of the left hand side expression.

Now we can apply step 4, divide by the other factor

And if I write it as text      x = (z-y)/(1-b)      brackets for the usual reason.

Here's some to try:

Q4. 2a + 2b = xa + yb      Make b the subject.

Q5. t + r = 3t                   Make t the subject.

Q6. u = at - 2t                  Make t the subject.

Q7. 2h + hg = 7g - 9         Make g the subject.

In each case choose some numbers to make a correct equation at the start and then test out your answer to see if the numbers work out correctly.

Bob

Ok.  Here we go.  For all 'linear' equations these four steps seem to always work.  I'll come back later to what 'linear' means and what you do when an equation isn't linear.

Mostly you won't need all four steps so rather than throwing you in at the deep end I'll introduce them as needed.

The problem you started with needs steps 2 and 4.

Step 2: Get all 'b' containing terms on the left and everything else on the right.

So this step isolates the 'b' term on its own.

Step 4: Divide by the other factor for b.

In our case we have 2b and we want just b, so divide by 2

Here's another example.  In Newtonian mechanics there's a formula:

Here v is the final velocity, u the initial velocity, a the constant acceleration, and t is time.

Let's make t the subject.

Step 2:

Step 4:

Here's some for you to try:

Q1. Using that formula make a the subject.

Q2.  y = mx + c. Make c the subject.

Q3 Same formula, make x the subject.

Let's let that sink in and then I'll move on the step 3.

Bob