18x + 9 10x - 4
________ > _________
3 2
18x + 9 / 3 > 10x - 4 / 2
18x + 9 10x - 4
18 = -9 10x = 4
x = -9/18 x = 4/10
x = -1/2 x = 2/5
-1/2 < 2/5
or
2/5 > -1/2
is this what you need ?
(18x+9)/3 > (10x-4)/2
multiply by 6
2(18x + 9) > 3(10x-4)
36x + 18 > 30x - 12
6x > -30
x > -5
To compare these two fractions, we need to find a common denominator. In this case, the common denominator is 6, which is the least common multiple of 3 and 2.
To find the equivalent fractions with a denominator of 6, we need to multiply both the numerator and denominator of each fraction by a suitable factor.
For the first fraction, multiply both the numerator and denominator by 2:
(18x + 9) * 2 = 36x + 18
3 * 2 = 6
So, the first fraction becomes (36x + 18) / 6.
For the second fraction, multiply both the numerator and denominator by 3:
(10x - 4) * 3 = 30x - 12
2 * 3 = 6
So, the second fraction becomes (30x - 12) / 6.
Now that the fractions have the same denominator, we can compare the numerators to determine the inequality.
We have:
(36x + 18) / 6 > (30x - 12) / 6
Since the denominators are the same, we can eliminate them from the inequality:
36x + 18 > 30x - 12
Now, let's simplify the inequality by combining like terms:
Collecting the x-terms on one side and the constant terms on the other side, we get:
36x - 30x > -12 - 18
6x > -30
Divide both sides of the inequality by 6 to isolate x:
x > -30/6
Simplifying, we find:
x > -5
Therefore, the solution to the inequality is x > -5.