AS Maths Help - GCSE Algebra?

Question

Ive just started AS maths, and ive been given some gcse algebra questions, problem is, ive been out of education for 3 years, and although i got an A at gcse, i cant remember at ALL how to do most of these questions. I would ask the teacher but i have to work full time this week so im missing out on lessons and cant go into college to ask for help, so ive come here :).

Just some stuff i need to know...

what does it mean by factorise? (and difference between factorise and factorise fully?)

Solving inequality 2x+3>4x+5

I cant do this equation, 2x^2+3x-7=0 and this one 2(x+1)^2 / 10(x+1)

Explain why 9^3/2=27

The list goes on, i would prefer to be told how to do these than just be told the answer as i really need to remember, thanks for any help!

Answer 1

Keep studying math, it's great! So, let's take it one step at a time.

First, factorise (we say factor in the US, but whatever) and factorise fully are really the same thing (fully is just a reminder to be careful on a problem, b/c there might be more than one or two steps). It means you take out common factors, such as the following: x^2+x = x(x+1). Then, you use some basic rules that you can review from any basic high school algebra textbook, such as: x^2-9 = (x-3)(x+3).

Solving inequalities is nothing to be scared of. Just take the variable to one side and simplify. 2x + 3 > 4x + 5 ---> 2x - 4x > 5 - 3 ---> -2x > 2 -----> x < -1 (remember to flip inequality sign is you are multiplying or dividing by a negative number). Well, that's it!

2x^2 + 3x - 7 = 0 should be done with the quadratic formula (look it up if you need more help. If you have something of the form ax^2+bx+c = 0, the formula is (-b +/- [you may have two solutions] sqrt(b^2 -4*a*c))/(2a). In your case, a = 2, b = 3, c = -7. Just plug in and solve. If you have something invalid such as a negative number under the square root, the equation has no real number solution, which is also a valid answer.

To simplify 2(x+1)^2/(10(x+1)), just write it out completely to not get confused: 2*(x+1)*(x+1)/(10(x+1)). Cross out one of the x+1 from both top and bottom and divide both top and bottom by 2 to get: (x+1)/5. If you want to be completely accurate, remember to note that x Does Not Equal -1, since that would mean that you were dividing by 0.

9^(3/2) = (9)^[(1/2)*3]. 9^1/2 = sqrt(9) = 3, and 3^3 = 27.

Hope this helps, and happy solving!