How do you solve $\frac{5}{6} (12 p + 4) = - 13 p + 4$ $5/6(12p+4)=-13p+4$ ?

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How do you solve $\frac{5}{6} (12 p + 4) = - 13 p + 4$ $5/6(12p+4)=-13p+4$ ?

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Answer 1 · 2017-01-26T15:16:25

See the entire solution process below:

Explanation:

First, multiply both sides of the equation by $6$ $color(red)(6)$ to eliminate the fraction and keep the equation balanced:

$6 \times \frac{5}{6} (12 p + 4) = 6 (- 13 p + 4)$ $color(red)(6) xx 5/6(12p + 4) = color(red)(6)(-13p + 4)$

$cancel(color(red)(6)) xx 5/color(red)(cancel(color(black)(6)))(12p + 4) = color(red)(6)(-13p + 4)$

$5(12p + 4) = color(red)(6)(-13p + 4)$

$60p + 20 = -78p + 24$

Next add $color(red)(78p)$ and subtract $color(blue)(20)$ from each side of the equation to isolate the $p$ terms while keeping the equation balanced:

$60p + 20 + color(red)(78p) - color(blue)(20) = -78p + 24 + color(red)(78p) - color(blue)(20)$

$60p + color(red)(78p) + 20 - color(blue)(20) = -78p + color(red)(78p) + 24 - color(blue)(20)$

$138p + 0 = 0 + 4$

$138p = 4$

Now, divide each side of the equation by $color(red)(138)$ to solve for $p$ while keeping the equation balanced:

$(138p)/color(red)(138) = 4/color(red)(138)$

$(color(red)(cancel(color(black)(138)))p)/cancel(color(red)(138)) = 2/69$

$p = 2/69$

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How do you solve $\frac{5}{6} (12 p + 4) = - 13 p + 4$ $5/6(12p+4)=-13p+4$ ?

1 Answer

Explanation:

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