Find the integer values of x that satisfy both of these inequalities.
2 answers:
Answer:
x ∈ [-2/3, 3)
Step-by-step explanation:
5 − 3x ⩽ 7 and 4x + 1 < 13, this is given
-3x ≤ 7-5 and 4x < 13 -1, subtract 5 from first inequality and subtract -1 from second
-3x ≤ 2 and 4x < 12, combine like terms
x ≥ -2/3 and x < 12/4, divide by -3 and change the first inequality, and divide the second inequality by 4
x ≥ -2/3 and x < 3
[-2/3, ∞) and (-∞, 3)
x ∈ [-2/3, 3)
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now, if he increases his speed by 2 mph, then his new speed is "r + 2", and he arrives there 4 hours earlier, so if he took "t" hours going at "r" speed, then when he's going faster at "r + 2", he only takes "t - 4" hours, for the same 48 miles.
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so, in his usual speed, say is hmm "r" mph, so in his usual "r" speed, he rolls on for the 48 miles and it takes him "t" hours to get there.
now, if he increases his speed by 2 mph, then his new speed is "r + 2", and he arrives there 4 hours earlier, so if he took "t" hours going at "r" speed, then when he's going faster at "r + 2", he only takes "t - 4" hours, for the same 48 miles.
it cannot be a negative value, since is just a forward speed rate, so can't be -6.