Let’s take this one problem at a time

1)logx+log(x-3)=1

*Remember since no base is given you are therefore using base 10

For this we use the formula log m + log n = log (m*n)

Here we have m = x and n = (x – 3)

logx+log(x-3)=1 Write original equation

log [ x * ( x – 3)] = 1

10 log [ x * ( x – 3)] = 10 1 Exponentiate each side using base 10

[ x * ( x – 3)] = 10

x2 – 3x = 10

x2 – 3x – 10 = 0Rewrite in simple form

(x – 5) (x + 2) = 0Factor

*Remember the zero product property: when ab = 0, the a = 0, b= 0, or both = 0

(x-5) = 0(x + 2) = 0 Solve both

x = 5x = -2

Check both answers:

When x = 5

log5+log(5-3)=1

log5+log(2)=1

1 = 1

When x = 2

log2+log(2-3)=1

log2+log(-1)=1

log (-1) is not defined, so not a real solution

2)(x+3)(x-3)>0

Use the zero product property as above, just use > instead of =

(x + 3) > 0, subtract 3 from both sides

x < -3 (x-3) > 0, add 3 to both sides

x > 3

You could also graph this one to see which direction to “shade” if you need to graph it as well.

3)|x – 3| < 7 The trick here is to remember that you need both the positive AND the negative values. The positive value: |x – 3| < 7 x – 3 < 7, add three to both sides x < 10 The negative value: (because you set it “equal” to a negative number) *Don’t forget that when you set this to the negative value you need to reverse the inequality sign* x – 3 > -7, add 3 to both sides

x > -4

Your final answer is: -4 < x < 10 Hope this helped!! If you are still confused I would suggest getting some extra problem sets from your teacher so you don’t fall too far behind before the school year starts off. Good luck!

All answer are incorrect or in part staggering! The is a try no rely if the equation holds. because of the fact the quotient x/x is given, the equation is defined for x=0, because of the fact the reality, that there is a genuine decrease for x goint to 0 of x/x: limit_x->0 x/x=a million. So get rid of the quotient a minimum of for x unequal 0. The equation now is x+x²=x². This equation could be rearranged via unique arithmetic operations. It supplies x=0. stupid or. What does is advise? The equation does not carry for x unequal 0. it somewhat is it. it may returned be simplified a million+x=x or a million=0, it somewhat is inaccurate. For 0 is holds interior the stable form and interior the decrease attention: 0/0+0=a million+0 unequal 0. The equation does not be valid for any actual numbers!

x=5

x>3 or x<-3 -4