olve. State the solution set using interval notation and graph it
1/3x > 2 and 1/4x > 2
First should I solve for x. How would you handle this problem?
yes, solve for x in each..
x>6; x>8
so if the second condition is met, that is x is g reater than eight, the first is not applicable.
first solve each of the inequalities
here is the first:
1/3x > 2
1 > 6x
6x<1
x<1/6
in the same way from the second, x<1/8
Also it should be obvious that x cannot be zero or a negative, since 1/(a negative) is not greater than 2
so we have x<1/6 AND x<1/8
so the only values that would work are
0 < x < 1/8
See how important it is to use proper notation?
if you meant (1/3)x > 2 and (1/4)x > 2
then bobpursley's solution is correct
if you meant 1/(3x) > 2 and 1/(4x) > 2
then my solution is correct.
5N+3-4NGRAETER THEN -5-3N
To solve the inequality 5N + 3 - 4N > -5 - 3N:
Combine like terms on both sides of the inequality:
5N - 4N - 3N > -5 - 3 - 3N
Simplify:
-2N > -11 - 3N
Add 3N to both sides:
-2N + 3N > -11 - 3N + 3N
N > -11
The solution to the inequality is N > -11.
In interval notation, this would be written as (-11, ∞).
To solve the equation 5N + 3 - 4N > -5 - 3N, we need to simplify and isolate the variable N on one side of the inequality sign.
Let's start by combining like terms on both sides of the equation:
5N - 4N + 3N > -5 - 3 - 3N
Simplifying further, we have:
4N > -8 - 3N
Next, we want to isolate the variable N on one side, so let's move the -3N term to the left side by adding 3N to both sides:
4N + 3N > -8
Combining like terms again, we get:
7N > -8
Now, to solve for N, we divide both sides of the inequality by 7:
N > -8/7
The solution for N is N > -8/7.
In interval notation, we represent this solution as (-8/7, +∞), which means N is greater than -8/7 and can take any value larger than that.
To graph this solution on a number line, we start at -8/7 and shade everything to the right since N is greater than -8/7.