Find the unknown numbers.
One number is nine less than another. Their sum is negative twenty-seven.

Solve the equation.

$\frac{9}{2}+\frac{1}{4}(x+2)=\frac{3}{4}x$

Find the unknown number.

If half of a number is added to $\frac{2}{5}$, the result is the same as subtracting $\frac{1}{10}$ from the number.

Patricia has $30$ meters of fencing to make a rectangular garden in her backyard. She wants the length to be $5$ meters more than the width. Complete steps $1$ & $2$ of the word problem solving process to set up an equation Patricia could use to find the width of her rectangular fence.

Jordan is designing a picture frame for a poster. The perimeter of the frame is $80\mathrm{cm}$. The length is $12\(\operatorname{cm}\)$ longer than its width. Identify the dimensions of this poster.

Solve the Equation.

$3(2-5x)=4x+25$