+1/3)+10(1/2k−1).(1 point) Responses 1912k−23 19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction 14k−7 14 k minus 7 14k−23 14 k minus Start Fraction 2 over 3 End Fraction 14k+13
To simplify the expression, we can start by distributing the 10 to both terms inside the parentheses:
(1/3) + 10 * (1/2k - 1)
= 1/3 + 10/2k - 10
Next, we can simplify the fractions:
= 1/3 + 5/k - 10
To add the fractions, we need a common denominator. The common denominator here is 3k:
= k/3k + 15/3k - 10
Now, we can combine the fractions:
= (k + 15 - 30k)/3k
= (15 - 29k)/3k
So, the simplified expression is (15 - 29k)/3k.