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Solve for k in the equation: (7k+1)/6 = (3k−1)/2

Mathematics

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Answer

k=2k=2

Step-by-step solution

6 steps

let's solve for kk.

The given equation is:

7k+16=3k−12\frac{7k+1}{6} = \frac{3k-1}{2}

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators (6 and 2), which is 6, to eliminate the fractions.

    6×(7k+16)=6×(3k−12)6 \times \left(\frac{7k+1}{6}\right) = 6 \times \left(\frac{3k-1}{2}\right)

  2. Simplify both sides.

    7k+1=3(3k−1)7k+1 = 3(3k-1)

  3. Distribute the 3 on the right side.

    7k+1=9k−37k+1 = 9k-3

  4. Subtract 7k7k from both sides to gather kk terms on one side.

    1=9k−7k−31 = 9k - 7k - 3 1=2k−31 = 2k - 3

  5. Add 3 to both sides to isolate the term with kk.

    1+3=2k1 + 3 = 2k 4=2k4 = 2k

  6. Divide by 2 to solve for kk.

    42=k\frac{4}{2} = k 2=k2 = k

    The value of kk is:

    k=2k=2
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