Solve by adding seven on both sides of the equation.  This will isolate \(\displaystyle x\) on both sides of the equation.

\(\displaystyle -7+x +(7) = 2+(7)\)

Add the left side of the equation.

\(\displaystyle x=2+7\)

Add the right side of the equation.

\(\displaystyle x=9\)

The answer is \(\displaystyle 9\).

To solve this equation, we must isolate \(\displaystyle x\) on the left side by multiplying each side by \(\displaystyle 4\), as follows:

\(\displaystyle \frac{x}{4}=-9\)

\(\displaystyle 4(\frac{x}{4})=(-9)(4)\)

\(\displaystyle x=-36\)

Therefore, the correct answer is \(\displaystyle x=-36\).

When solving for x, we want x to be alone.  Therefore, in the equation

\(\displaystyle x - 12 = 9\)

we add 12 to both sides. 

\(\displaystyle x - 12 + 12 = 9 + 12\)

\(\displaystyle x = 21\)

To solve for \(\displaystyle x\), we must isolate it to one side of the equation, as follows:

\(\displaystyle x-241=241\)

\(\displaystyle x-241+241=241+241\)

\(\displaystyle x=482\)

In order to find the solution we must isolate the variable m. The first step is to subtract 346 from both sides as follows:

\(\displaystyle 346 - 346 + m = 1111 - 346\)

\(\displaystyle 0 + m = 765\)

\(\displaystyle m = 765\)

We can check the answer by plugging in our solution of 765 into the original equation. 

\(\displaystyle 346 + 765 = 1111\)

\(\displaystyle 1111 = 1111\)

It works.

\(\displaystyle -7x=-35\)

\(\displaystyle \frac{-7x}{-7}=\frac{-35}{-7}\)

\(\displaystyle x=5\)

Isolate the variable to one side.

Multiply each side by \(\displaystyle \frac{2}{3}\):

\(\displaystyle \frac{x}{\frac{2}{3}}=6\)

\(\displaystyle \frac{x\frac{2}{3}}{\frac{2}{3}}=\frac{6}{1}*\frac{2}{3}\)

Simplify and reduce:

\(\displaystyle x=4\)

The goal is to isolate the variable on one side.

\(\displaystyle \frac{x}{\frac{4}{5}} = 2\)

The opposite operation of division is multiplication, therefore , multiply each side by \(\displaystyle \frac{4}{5}\):

\(\displaystyle \frac{\frac{4}{5}x}{\frac{4}{5}} = \frac{4}{5}\times 2\)

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

\(\displaystyle 1\times x = \frac{4}{5} \times 2\)

The identity law of multiplication takes effect and we get the solution as:

\(\displaystyle x = \frac{8}{5}\)

The goal is to isolate the variable on one side.

\(\displaystyle \frac{6}{7} x = 3\)

The opposite operation of multiplication is division, therefore, we can either divide each side by \(\displaystyle \frac{6}{7}\) or multiply each side by its reciprocal \(\displaystyle \frac{7}{6}\):

\(\displaystyle \frac{7}{6}\times \frac{6}{7}x = \frac{7}{6}\times 3\)

The left hand side can be reduced by recalling that anything multiplying a fraction by its reciprocal is equal to 1:

\(\displaystyle 1\times x = \frac{7}{6} \times 3\)

The identity law of multiplication takes effect and we get the solution as:

\(\displaystyle x = \frac{21}{6}\)

However, this solution can be reduced by dividing both the numerator and denominator by 3:

\(\displaystyle x = \frac{7}{2}\)