SOLUTION: Find all real numbers t such that 2/3t - 1 < t + 7 ≤ -2t + 15. Give your answer as an interval.
Algebra.Com
Question 1083260: Find all real numbers t such that 2/3t - 1 < t + 7 ≤ -2t + 15. Give your answer as an interval.
Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Interval for which t satisfies the inequalities is ( -24, 8/3]
—
Found by: —> —>
and —> —>
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
break these up into 2 separate inequalities.
start with 2/3 * t - 1 < t + 7 <= -2t + 15
the first set of inequalities is:
2/3 * t - 1 < t + 7
add 1 to both sides to get:
2/3 * t < t + 8
subtract t from both sides to get:
2/3 * t - t < 8
simplify to get:
-1/3 * t < 8
multiply both sides by 3 to get:
-t < 24
multiply both sides by -1 to get:
t > -24
multiplying both sides by -1 reverses the inequality.
solution for the first set of inequalities is t > -24
the second set of inequalities is:
t + 7 <= -2 * t + 15
subtract 7 from both sides to get:
t <= -2 * t + 8
add 2t to both sides to get:
3 * t <= 8
divide both sides by 3 to get:
t <= 8/3
solution for the second set of inequalities is t <= 8/3
your solution is that t > -24 and t <= 8/3
this can be written as -24 < t <= 8/3
in interval notation, this would be written as:
(-24,8/3]
you can test this out with various values of t to ensure the inequality is correct.
the inequality statement to test is:
2/3 * t - 1 < t + 7 <= -2t + 15
in order for the statement to be true, all parts of the inequality must be true.
2/3 * t - 1 must be smaller than t + 7 AND t + 7 must be smaller than or equal to -2t + 15
i checked and it all looks good, so i'm reasonably certain that the solution is good.
RELATED QUESTIONS
Find all real numbers s such that -2(s - 7) > 4s + 8. Give your answer as an... (answered by CubeyThePenguin)
Find all real numbers s such that -2(s-7) is greater than 4s+8. Give your answer as an... (answered by Boreal)
Find all real numbers x such that 3x - 7 (is less than or equal to) 5x +9. Give your... (answered by tommyt3rd)
Solve \frac{1}{3} t - 5 < t + 2 - 5t + 10. Give your answer as an... (answered by mccravyedwin)
Solve the system. Enter answer as an ordered pair (t,v).
1/2t - 1/5v = 5/2
2/3t + 1/4v... (answered by stanbon)
Solve the equations below exactly. Give your answers in radians, and find all possible... (answered by ikleyn)
2(t-5)-3(2t-7)=12-5(3t+1) (answered by jim_thompson5910)
Solve the system. (Give your answer as an improper fraction. If the system has infinitely (answered by stanbon)
Find a number t such that the distance between (-2,2) and (3t,2t) is as small as... (answered by Fombitz)