Help my daughter with her Algebra homework?

Question

My 16 yr old is doing her math H/W and is stuck - now we have the answer but she needs to show the workings etc. The question is as follows - This is my daughter asking now -

put xh (x) + 1 = 0 into the function hx: is 2 -3x

acc to the book the answer is -1/3 (1 over 3 as a fraction) but somehow i keep getting 1/4 or 1/2 (fractions) help?

Hi Msmaths, Thank you for your help, she is just going through it now, but she is having trouble getting it - she bit scared, you don't teach in Ireland do u?

ironduke8159 - She has written the question out as presented in her math book - concise maths for Junior cert higher level.

Answer 1

h(x) = 2 - 3x

If x*h(x) + 1 = 0, then
x*(2-3x) + 1 = 0
2x - 3x^2 + 1 = 0
Multiply both sides by -1 and rearrange in descending order.
3x^2 - 2x - 1 = 0
Factor or use the quadratic formula.
This one factors. You are looking for factors of -3 that add up to -2. Those are -3 and +1.
3x^2 - 3x + x - 1 = 0
3x(x-1) + 1(x-1) = 0
(3x+1)(x-1) = 0
3x+1 = 0 or x-1 =0
x = -1/3 or x = 1

Answer 2

I think you mean h(x)=2-3x, and you want to find h(x+1)=0 ?
At least that's where I got -1/3.

if h(x) = 2 - 3x, then h(x+1) = 2 - 3(x+1).

2 - 3(x+1) = 0
add 3(x+1) to both sides to get
3(x+1) = 2
distribute the 3
3x + 3 = 2
subtract 3 both sides
3x = -1
divide by 3
x = -1/3

that what you looking for?

Answer 3

xh(x)+1=0
x(2-3x)+1=0
2x-3x^2+1=0, divide both sides by -1
3x^2-2x-1=0, put -2=-3+1 in the coefficient of x
3x^2-3x+1x-1=0
3x(x-1)+1(x-1)=0
(x-1(3x+1)=0, x-1=0 or 3x+1=0
x=1,-1/3. ANS.
I hope your daughter gets happy.

Answer 4

Does xh =hx? I really cannot understand your terminology.
What does xh(x) mean? How does one put an equation into a function? If you could write the problem precisely as it was originally written, we can be of help.

Answer 5

Multiply the contents of the bracket by the number outside. Therefore 5(d+3) = 5d +15

Answer 6

did you divide the right numbers? maybe you miss calcuated