Solve the compound inequality. x+3<0 or 5x>−10
2 answers:
Answer:
<em>x</em> < – 3 or <em>x</em> > – 2
Step-by-step explanation:
For <em>x </em>+ 3 < 0 :
subtract 3 from both sides of the inequality:
x + 3 – 3 < 0 – 3
x + 0 < – 3
x < –3
For 5<em>x</em> > – 10:
Divide both sides of the inequality by 5 to isolate x:
x > –2
Therefore:
<em>x </em>< – 3 or <em>x</em> > –2
Interval notation: [(– ∞, –3) ∪ (–2, ∞)]
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Answer:
(x, y) = (1/2, -1)
Step-by-step explanation:
Subtracting twice the first equation from the second gives ...
(2/x +1/y) -2(1/x -5/y) = (3) -2(7)
11/y = -11 . . . . simplify
y = -1 . . . . . . . multiply by y/-11
Using the second equation, we can find x:
2/x +1/-1 = 3
2/x = 4 . . . . . . . add 1
x = 1/2 . . . . . . . multiply by x/4
The solution is (x, y) = (1/2, -1).
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<em>Additional comment</em>
If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.
A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).
