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How do you solve #|-6t+3|+9 \ge 18#?

Answer 1

#t<=-1# OR #t>=2#

#|-6t+3|>=9# subtract 9 from both sides #-6t+3>=9# OR #6t-3>=9# separate into two equations #-6t>=6# OR #6t>=12# #t<=-1# OR #t>=2#

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Answer 2

Kennedy Adams

To solve the inequality ( |-6t+3| + 9 \geq 18 ), we follow these steps:

Subtract 9 from both sides of the inequality: [ |-6t+3| \geq 9 ]
Split the inequality into two cases: a) ( -6t+3 \geq 9 ) b) ( -(-6t+3) \geq 9 )
Solve each case separately: a) ( -6t+3 \geq 9 ) Subtract 3 from both sides: [ -6t \geq 6 ] Divide by -6 (note the reversal of the inequality when dividing by a negative number): [ t \leq -1 ]

b) ( -(-6t+3) \geq 9 ) Simplify the inequality: [ 6t - 3 \geq 9 ] Add 3 to both sides: [ 6t \geq 12 ] Divide by 6: [ t \geq 2 ]

Therefore, the solution to the inequality ( |-6t+3| + 9 \geq 18 ) is ( t \leq -1 ) or ( t \geq 2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.