# College Algebra : Linear Equations

## Example Questions

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### Example Question #1 : Linear Equations

Solve for :

Explanation:

can be simplified to become

Then, you can further simplify by adding 5 and  to both sides to get .

Then, you can divide both sides by 5 to get .

### Example Question #2 : Linear Equations

Solve for :

Explanation:

To solve for , you must first combine the 's on the right side of the equation. This will give you .

Then, subtract  and from both sides of the equation to get .

Finally, divide both sides by  to get the solution .

### Example Question #3 : Linear Equations

Solve the following equation for :

Explanation:

The first step is to distribute (multiply) the 2 through the parentheses:

Then isolate  on the left side of the equation. Subtract the 10 from the left and right side.

Finally, to isolate , divide the left side by 2 so that the 2 cancels out. Then divide by 2 on the right side as well.

You can verify this answer by plugging the  into the original equation.

### Example Question #4 : Linear Equations

Solve for :

Explanation:

Combine like terms on the left side of the equation:

Use the distributive property to simplify the right side of the equation:

Next, move the 's to one side and the integers to the other side:

### Example Question #5 : Linear Equations

Solve for x:

Explanation:

Simplify the parenthesis:

Combine the terms with x's:

Combine constants:

### Example Question #3 : Linear Equations

Solve the following equation when y is equal to four.

Explanation:

Solve the following equation when y is equal to four.

To solve this equation, we need to plug in 4 for y and solve.

### Example Question #6 : Linear Equations

Solve the following:

Explanation:

To solve, we must isolate x. In order to do that, we must first add 7 to both sides.

Next, we must divide both sides by 3.

### Example Question #7 : Linear Equations

Write an equation of the line passing through (5,10) and (10,2).

None of these.

Explanation:

To find this line, first find the slope (m) between the two coordinate points. Then use the point-slope formula to find a line with that same slope passing through a particular point.

### Example Question #8 : Linear Equations

Solve for .

Explanation:

First distribute out each side of the equation.

simplifies to .

Now for the right hand side,

becomes .

Now we equate both sides.

,

### Example Question #9 : Linear Equations

Solve for .

Explanation:

First, we need to simplify what's inside the parentheses.

Now we continue to evaluate the left hand side.

The right hand side does not need any reduction.

We set the two sides equal to each other.

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