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Anonymous asked in Science & MathematicsMathematics · 1 year ago

# The equation is 13k = 6k/15t - 7t Make k the subject?

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• 13 k = 6 k/15 t - 7t

13 k = (2 k t)/5 - 7 t

65 k = t (2 k - 35)

k(65 - 2 t) = -35 t

k

= -35 t / (65 - 2 t)

= 35 t / (2 t - 65)

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• 13k = 6k/15t - 7t

// Multiply through by 15t

13k (15t) = 6k - 7t (15t)

195 kt - 6k = - 105 t²

// Factor out k

k (195t - 6) = -105 t²

// Divide through by (195t - 6)

k = -105 t² / (195t - 6)....................ANS

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• Presentation is open to doubt due to lack of brackets.

• No it isn't! That's why we use the order of operations, to prevent ambiguity. Asker my have asked the wrong question but what was asked is NOT in doubt.

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• I assume that the - 7t is a separate term

in other words, your equation is NOT:

13k = 6k / (15t - 7t)

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13k = (6k/15t) - 7t

multiply both sides by (15t)

(13k)(15t) = 6k - (15t)(7t)

clean up

195kt = 6k - 105t^2

subtract 6k from both sides

195kt - 6k = -105t^2

factor out "k" on the left

k(195t - 6) = -105t^2

divide both sides by (195t - 6)

k = (-105t^2) / (195t - 6)

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• Presuming you mean:

13k = 6k/(15t) - 7t

Since "k" is in more than one term, we need to group them together. Start with multiplying both sides by the denominator (15t):

195kt = 6k - 105t²

Now move the terms with "k" to one side and all other terms to the other side:

195kt - 6k = -105t²

to simplify a little, multiply both sides by -1. I'll flip the two terms around the subtraction on the left side:

6k - 195kt = 105t²

And now I can divide both sides by 3 to simplify further before we move on:

2k - 65kt = 35t²

Now we can factor out the k:

k(2 - 65t) = 35t²

and divide:

k = 35t² / (2 - 65t)

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