To solve for \(\displaystyle 4\frac{2}{3}-3\frac{1}{12}\), the fractions should first be converted to ones that share a common denominator. Given that \(\displaystyle 3\cdot4=12\), the common denominator is 12. 

Thus, \(\displaystyle 4\frac{2}{3}\) can be converted to \(\displaystyle 4\frac{8}{12}\). This gives us:

\(\displaystyle 4\frac{8}{12}-3\frac{1}{12}=1\frac{7}{12}\)

It is easiest to begin by moving like terms together. Hence:

\(\displaystyle 4x-2a+3ax-5x+4a-12x\)

becomes

\(\displaystyle 4x-5x-12x-2a+4a+3ax\)

(Notice that \(\displaystyle ax\) is its own term.)

Now, consider the coefficients for each term.

For \(\displaystyle x\), you have \(\displaystyle 4-5-12 = -13\)

For \(\displaystyle a\), you have \(\displaystyle -2+4=2\)

Hence, the expression simplifies to:

\(\displaystyle -13x+2a+3ax\)

This can be moved around to get the correct answer (which means the same thing):

\(\displaystyle 2a-13x+3ax\)

Begin by distributing the two groups. Notice that you must distribute the subtraction through the groups:

\(\displaystyle 4x-3(a+x)-4a(x+5)\)

becomes

\(\displaystyle 4x-3a-3x-4ax-20a\)

Next, you should move like terms next to each other:

\(\displaystyle 4x-3x-3a-20a-4ax\)

(Notice that \(\displaystyle -4ax\) is its own term.)

Now, combine terms.

For \(\displaystyle x\), you get \(\displaystyle 4-3 = 1\)

For \(\displaystyle a\), you get \(\displaystyle -3-20 = -23\)

Therefore, the final form of the expression is:

\(\displaystyle x-23a-4ax\)

Begin by distributing. Thus,

\(\displaystyle 5(x+7a) = 14x-3(2x-5)\)

becomes

\(\displaystyle 5x+35a = 14x-6x+15\)

(Don't forget that you have to distribute your subtraction for the second group.)

Combine like terms on the right side of the equation:

\(\displaystyle 5x+35a = 8x+15\)

Next, move the \(\displaystyle x\) values to the left side of the equation and all of the other values to the right side:

\(\displaystyle 5x -8x = 15-35a\)

Combine like terms on the left:

\(\displaystyle -3x = 15-35a\)

Finally, divide everything by \(\displaystyle -3\):

\(\displaystyle \frac{-3x}{-3} = \frac{15-35a}{-3}\)

This comes out to be:

\(\displaystyle x = -5+\frac{35a}{3}\)

or

\(\displaystyle x = \frac{35a}{3}-5\)

Begin by distributing the multiplied groups:

\(\displaystyle ax^2 +x^2+24ax-12ax-4ax^2-4xb\)

Next, move all similar factors together:

\(\displaystyle x^2+24ax-12ax+ax^2-4ax^2-4xb\)

Now, combine each set of similar factors:

\(\displaystyle 24ax-12ax = 12ax\)

\(\displaystyle ax^2-4ax^2 = -3ax^2\)

Therefore, our answer is:

\(\displaystyle x^2+12ax-3ax^2-4xb\)

This problem is not too difficult. Begin by moving all common terms next to each other:

\(\displaystyle 4g-12g+12g+13g-7ag-15ag+14ta-2ta-4ta+15t\)

Next, simplify each group of terms that has the same set of variables:

\(\displaystyle 4g-12g+12g+13g=17g\)

\(\displaystyle -7ag-15ag=-22ag\)

\(\displaystyle 14ta-2ta-4ta = 8ta\)

And do not forget that you are left with \(\displaystyle 15t\) as well!

Now, combine all of these:

\(\displaystyle 17g-22ag+8ta+15t\)

Begin by moving common factors next to each other. Thus,

\(\displaystyle 8x^2-3x-123nx^2-14x^2+3nx-13nx^2+4x\)

becomes

\(\displaystyle 8x^2-14x^2-3x+4x-123nx^2-13nx^2+3nx\)

Now, combine each set:

\(\displaystyle 8x^2-14x^2=-6x^2\)

\(\displaystyle -3x+4x=x\)

\(\displaystyle -123nx^2-13nx^2=-136nx^2\)

Remember, there still is \(\displaystyle 3nx\) also.

Therefore, the simplified form of the expression is:

\(\displaystyle x-6x^2-136nx^2+3nx\) 

\(\displaystyle 5 < A < 7\)

\(\displaystyle 5 < C < 7\)

also, since \(\displaystyle 5 < B < 7\), it follows that 

\(\displaystyle -7 < -B < -5\)

\(\displaystyle A - B + C = A + (-B)+ C\), and by the inequality properties, 

\(\displaystyle A + (-B)+ C < 7 + (-5) + 7\)

\(\displaystyle A -B + C < 7 -5 + 7\)

\(\displaystyle A -B + C < 9\)

making 9 the greater quantity.