SOLUTION: Solve the polynomial inequality. Express the solution set in interval notation. {7}/{x + 3} > {8}/{x - 3}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the polynomial inequality. Express the solution set in interval notation. {7}/{x + 3} > {8}/{x - 3}      Log On


   

Question 946019: Solve the polynomial inequality. Express the solution set in interval notation.
{7}/{x + 3} > {8}/{x - 3}
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Make a relation to 0.

7%2F%28x%2B3%29%3E8%2F%28x-3%29

7%2F%28x%2B3%29-8%2F%28x-3%29%3E0

Multiply left and right members the lcd of (x+3)(x-3).

%287%2F%28x%2B3%29-8%2F%28x-3%29%29%28x%2B3%29%28x-3%29%3E0%2A%28x%2B3%29%28x-3%29

7%28x-3%29-8%28x%2B3%29%3E0, hoping you can see through the skipped step;

7x-21-8x-24%3E0
-x-45%3E0
-x%3E45
highlight%28x%3C-45%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the polynomial inequality. Express the solution set in interval notation.
{7}/{x + 3} > {8}/{x - 3}


7%2F%28x+%2B+3%29+%3E+8%2F%28x+-+3%29

7(x - 3) > 8(x + 3) ------- Multiplying by LCD, (x + 3)(x - 3)

7x - 21 > 8x + 24

7x - 8x > 24 + 21

- x = 45

%28-+x%29%2F%28-+1%29+%3C+45%2F%28-+1%29 ------ Inequality sign changes when DIVIDING by negative number

highlight_green%28x+%3C+-+45%29