First, add \(\displaystyle \dpi{100} 200+50=250\).

Next, divide \(\displaystyle \dpi{100} 250\div 5=50\).

So \(\displaystyle \dpi{100} x=50\)

When simplifying an expression, you must combine like terms. There are two types of terms in this expression: “x’s” and whole numbers.  Combine in two steps:

1) x’s:  \(\displaystyle -7x+4x-x=-4x\)

2) whole numbers:   \(\displaystyle -11+3=-8\)

The simplified expression is: \(\displaystyle -4x-8\).

To solve, insert \(\displaystyle -2\) for each \(\displaystyle x\):

\(\displaystyle -6(-2)^{2}+12(-2)+3=\)

Simplify:

\(\displaystyle -6(4)-24+3=\)

\(\displaystyle -24-24+3=-45\) 

*Common error: When solving this part of the equation  always remember the order of operations (PEMDAS) and square the number in the () BEFORE multiplying!

\(\displaystyle 5(-2)^{2}-14=6\)

First, you need to find what would make \(\displaystyle x\) and \(\displaystyle y\) true in their respective equations. \(\displaystyle x\) equals 1 and \(\displaystyle y\) equals 4. The next step is to add those together, which gives you 5. 

Nell's story fits best because if she bought 9 bags with 3 pieces each, that would be 27 total. This fits best with the \(\displaystyle 9\times 3=27\) equation.

Find the number that makes the equation true. 2 works because when plugged in, the left side of the equation becomes 13, making the whole equation true.

From the question, we know that \(\displaystyle 5\) plus a number equals \(\displaystyle \frac{3}{5}\) of \(\displaystyle 25\). In order to find out what \(\displaystyle \frac{3}{5}\) of \(\displaystyle 25\) is, multiply \(\displaystyle \frac{3}{5}\) by \(\displaystyle \frac{25}{1}\).  

\(\displaystyle \frac{3}{5}\times\frac{25}{1}=\frac{75}{5}\), or \(\displaystyle 15\).

The number we are looking for needs to be five less than \(\displaystyle 15\), or \(\displaystyle 10\).

You can also solve this algebraically by setting up this equation and solving:

\(\displaystyle 5+x=\frac{3}{5}\times25\)

\(\displaystyle 5+x=15\) 

Subtract \(\displaystyle 5\) from both sides of the equation.         

\(\displaystyle x=10\)

To solve for \(\displaystyle x\), we want to isolate \(\displaystyle x\), or get it by itself. 

\(\displaystyle 2x-2=10\)

Add \(\displaystyle 2\) to both sides of the equation.

\(\displaystyle 2x-2=10\)

    \(\displaystyle +2\)        \(\displaystyle +2\)

\(\displaystyle 2x=12\)

Now we need to divide both sides by the coefficient of \(\displaystyle x\), i.e. the number directly in front of the \(\displaystyle x\).

\(\displaystyle 2x=12\)

\(\displaystyle x=6\)

First, subtract the three from both sides:

\(\displaystyle 18-3=3x+3\left ( -3\right )\)

\(\displaystyle 15=3x\)

Then, divide by three on both sides:

\(\displaystyle \frac{15}{3}=\frac{3x}{3}\)

\(\displaystyle 5=x\)