GoldenLeaf

$${\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{6}}}{{\mathtt{7}}}}\right){\mathtt{\,-\,}}{\mathtt{3}}$$

First you distribute the -7/2.

$${\mathtt{\,-\,}}\left({\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}\left({\mathtt{2}}\right)\right) = -{\mathtt{7}}$$

$${\mathtt{\,-\,}}\left({\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{6}}}{{\mathtt{7}}}}\right)\right) = -{\mathtt{3}}$$

This makes the equation into something a bit more legible.

$$\left({\mathtt{\,-\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right){\mathtt{\,-\,}}{\mathtt{3}}$$

Then you just subtract 3.

$$\left({\mathtt{\,-\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,-\,}}{\mathtt{3}}\right)$$

$$\left({\mathtt{\,-\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{6}}\right)$$

At this point you can drop the parentheses and you have your most simplified answer: -7x - 6

5x + 7 = 42

The goal here is to isolate the 'x'. First, subtract 7 from both sides.

5x + 7 - 7 = 42 - 7

5x = 35

Divide by 5

5x/5 = 35/5

x = 7

The answer is 7.

A tyrannosaurus rex.

'Tis a sad tale...

Oh, and DragonSlayer, I live relatively close to there...

4^3(-3)^2 + 4^2(-3)^3 - (4 + (-3))

$${{\mathtt{4}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{\left(-{\mathtt{3}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\left(-{\mathtt{3}}\right)}^{{\mathtt{3}}}{\mathtt{\,-\,}}\left({\mathtt{4}}{\mathtt{\,-\,}}\left({\mathtt{3}}\right)\right) = {\mathtt{143}}$$

2(a + 1) - 5(a -1)

It's already in its most simplified form.

1/3 (5x - 6) = 3

(3) 1/3 (5x - 6) = (3) 3

5x - 6 = 9

5x - 6 + 6 = 9 + 6

5x = 15

5x/5 = 15/5

x = 3

$${{\mathtt{24}}}^{{\mathtt{2}}} = {\mathtt{576}}$$

y + 4 = 0

For this linear equation, simplifying is simple. Just subtract 4 from both sides.

y = -4

The line would be alone y = -4

3x - 6y = -3
2x - 3 = y

Make both sides even in terms of placement of variables.

3x + 3 = 6y

2x - 3 = y

Cancel out the 'x's.

6x + 6 = 12y

-6x + 9 = -3y

6 = 12y

9 = -3y

Combine like terms.

15 = 9y

Simplify.

5/3 = y

Plug in 'y' to either equation.

3x - 6(5/3) = -3

3x - 10 = -3

3x = 7

x = 7/3

The solution is (7/3, 5/3)

Heh, I got here a bit late it seems. Now it is past midnight, but a day later!

New riddle!

Whether it be on prison windows or on your phone

You can grab a drink, and I am often raised.

What am I?