Question

Solving the inequality: − 3 ( x − 2 ) <1/3

a) x< 5/3


b) x> 5/3


c) x< 7/5
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d) x> 7/3

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Answer 1

To solve the inequality -3(x - 2) < 1/3, distribute the -3, simplify the inequality, and isolate the variable x. The solution is x > 17/9.

This correct answer is d)

Step-by-step explanation:

Solving the Inequality: -3(x - 2) < 1/3

To solve this inequality, we need to isolate the variable x. First, distribute the -3 across the parentheses: -3x + 6 < 1/3. Then, subtract 6 from both sides: -3x < 1/3 - 6.

Next, simplify the right side of the inequality: -3x < 1/3 - 18/3. Combine the fractions: -3x < -17/3.

Finally, divide both sides by -3, remembering to reverse the inequality sign since we are dividing by a negative number: x > (-17/3) / -3.

Simplify the right side: x > 17/9. Therefore, the answer is x > 17/9.

This correct answer is d)