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How do you write an inequality and solve given "two thirds of a number added to six is at least twenty two"?

Answer 1

Eli Assouline

#x >= 24#

#"two-thirds of a number " rarr 2/3x#

#"added to " 6" " rarr 6+2/3x#

'Is at least' #22# means it can be equal to #22#, or more than #22#.

#6+2/3x >= 22#

#2/3x >= 22-6#

#2/3x >= 16#

#3/2 xx2/3x >= 3/2xx16#

#x >= 24#

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Answer 2

Ethan Adkins

To write the inequality and solve the given statement, follow these steps:

Let the number be represented by the variable x.
Write the expression for "two thirds of a number added to six": (2/3)x + 6.
Express the condition "is at least twenty two" as the inequality: (2/3)x + 6 ≥ 22.
Solve the inequality for x by isolating the variable.

Here's the step-by-step solution:

(2/3)x + 6 ≥ 22 Subtract 6 from both sides: (2/3)x ≥ 16 Multiply both sides by 3 to eliminate the fraction: 2x ≥ 48 Divide both sides by 2: x ≥ 24

Therefore, the solution to the inequality is x ≥ 24.

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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.