Solve easy equations

Question

Can anyone please help me with solving this equation; thanks!

$$ \displaystyle \frac{d+7}{3}+4\quad=\quad -\frac{5d}{4} $$

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My Steps

$1.$ Multiplied both sides by $3$ and $4$ to get rid of the division.

Giving me: $4(d + 7 + 4) = 3(-5d)$

$2.$ Multiplied out the brackets.

Giving me: $4d + 28 + 16 = -15d$

$3.$ Collected like terms.

Giving me: $4d + 44 = -15$d

$44 = -19d$

$d = -2.31$

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$d = -4$ apparently but I'm not sure how to get this answer

Answer 1

multiplying by $12$ we get $$4(d+7)+48=-15d$$ this is equivalent to $$4d+28+48=-15d$$ $$19d=-76$$ $$d=-4$$

Answer 2

You forgot to multiply the $4$ on the LHS by $3$ in your first step. Your equation after step $1$ should read: $$4(d+7+\color{red}{12})=3(-5d)$$ The rest is fine.

Answer 3

You have a (very common) mistake at step $1$. If you multiply by $3$ and after by $4$ you get $$4\times 3\left(\displaystyle \frac{d+7}{3}+4\right)\quad=4\times 3 \left(-\frac{5d}{4}\right)$$ $$4\left(d+7+\color{red}{ 3\times}4\right)=4\times 3 \left(-\frac{5d}{4}\right)$$