If \(\displaystyle 3a+9=4b\), and \(\displaystyle b=24\), the first step is to plug in \(\displaystyle 24\) as the value of \(\displaystyle b\). 

\(\displaystyle 3a+9=4\cdot24\)

\(\displaystyle 3a+9=96\)

Subtract \(\displaystyle 9\) from each side. 

\(\displaystyle 3a=87\)

Divide each side by 3. 

\(\displaystyle a=29\)

If \(\displaystyle 2w-13=5v\), and \(\displaystyle w=28\), the first step is to plug in \(\displaystyle 28\) for \(\displaystyle w\):

\(\displaystyle 2\cdot 28-13=5v\)

\(\displaystyle 48-13=5v\)

\(\displaystyle 35=5v\)

Divide each side by \(\displaystyle 5\). 

\(\displaystyle 7=v\)

\(\displaystyle v=7\)

The first step is to simplifying \(\displaystyle 5(3x-4)-4x(2\cdot 3)+13\) is to apply the distributive property to the first parenthetical.

\(\displaystyle 15x-20-4x(2\cdot 3)+13\)

Next, we reduce the multiplication expression in the second parenthetical.

\(\displaystyle 15x-20-4x(6)+13\)

\(\displaystyle 15x-20-24x+13\)

Next, we combine like terms.

\(\displaystyle -9x-7\)

To solve for the equation, follow the steps below:

\(\displaystyle 5x+4+3=27\)

\(\displaystyle 5x+7=27\)

Subtract \(\displaystyle 7\) from each side. 

\(\displaystyle 5x=20\)

Divide each side by \(\displaystyle 5\). 

\(\displaystyle x=4\). 

Therefore, \(\displaystyle 4\) is the correct answer.

To solve for \(\displaystyle y\), follow the steps below:

\(\displaystyle 6y+14=9y-3\)

Add \(\displaystyle 3\) to each side. 

\(\displaystyle 6y+17=9y\)

Subtract \(\displaystyle 6y\) from each side. 

\(\displaystyle 17=3y\)

Divide each side by \(\displaystyle 3\). 

\(\displaystyle y=\frac{17}{3}\)

Therefore, the correct answer is \(\displaystyle \frac{17}{3}\).

The first step to solving this equation is to make sure the fractions have common denominators. 

\(\displaystyle \frac{w}{8}+\frac{1}{4}=1\)

Given that \(\displaystyle \frac{1}{4}=\frac{2}{8}\), the equation can be rewritten as:

\(\displaystyle \frac{w}{8}+\frac{2}{8}=1\)

Since \(\displaystyle \frac{8}{8}\) is equal to \(\displaystyle 1\), the value of \(\displaystyle w\) must be \(\displaystyle 6\) because 

\(\displaystyle \frac{6}{8}+\frac{2}{8}=1\)

Therefore, \(\displaystyle 6\) is the correct answer. 

if 5 less than x is equal to 14, then \(\displaystyle x-5=14\).

To solve this, 5 should be added to each side of the equation, which results in \(\displaystyle x=19\). 

\(\displaystyle 7x-18=41+2^{2}\)

First, square 2: 

\(\displaystyle 7x-18=41+4\)

Next, add together 41 and 4:

\(\displaystyle 7x-18=45\)

Add 18 to both sides:

\(\displaystyle 7x=63\)

Divide both sides by 7: 

\(\displaystyle x=9\)

First, "move" all of the variables to one side of the equation:

\(\displaystyle 4x -10x - 3= 15\)

Next, "move" the other numbers to the right side of the equation:

\(\displaystyle 4x -10x = 15 + 3\)

Simplify:

\(\displaystyle -6x = 18\)

Now, divide both sides by \(\displaystyle -6\):

\(\displaystyle \frac{-6x}{-6} = \frac{18}{-6}\)

Thus, you get:

\(\displaystyle x = -3\)

Fill in the blank with a number that will make the equation true. On the right side, \(\displaystyle 8\times3=24\), so the left side needs to equal \(\displaystyle 24\) also. "Something" \(\displaystyle -9+12=24\). If you test the answers, \(\displaystyle 21\) is the number that makes the equation true, so \(\displaystyle 21\) is the correct answer.

Alternatively, \(\displaystyle \small -9 + 12\) is the same as \(\displaystyle 3\), so "something" \(\displaystyle +3=24\). That "something" would be \(\displaystyle 21\), so \(\displaystyle 21\) is the correct answer.