compound inequality
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(1) Does x = -5 satisfy the following compound inequality?
4 > -2(x+8) >= -6 AND 4 < 3x + 10 < 19
(2) Simplify the following compound inequality and express the result using interval notation:
7 < 3(x+2) + 10 < 25 AND 8 > 10 - 2x > 0
(3) Solve for x:
| x - 1/4 | = | (1/2)x - 3/4 |
(4) Solve the following system of linear equations using both additon and substitution and verify that you get the same answer in either case.
3x + y = 6
2x - 3y = 15
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A compound inequality is highlighted for expressions.
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1) Does x = -5 satisfy the following compound inequality?
4 > -2(x+8) >= -6 AND 4 < 3x + 10 < 19
Solution:
Put x = - 5 in -2(x + 8) = -2(-5 + 8) = -6
Thus it satisfies the first inequality 4 > -2(x+8) >= -6.
Now put x = -5 in 3x + 10 = 3(-5) + 10 = -5
But -5 does not lie between 4 and 19 do it does not satisfy the second inequality
4 < 3x + 10 < 19
Thus x = -5 does not satisfy the given compound inequality.
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