### All TACHS Math Resources

## Example Questions

### Example Question #1 : Inequalities

Solve the following inequality:

**Possible Answers:**

**Correct answer:**

In algebra an inequality is a relationship that holds through different values of a variable. An inequality is considered to be solved when the variable is isolated to one side of the inequality. We will do this by performing the reverse of the operations that were done to the variable. It is important to note that what is done to one side of the inequality needs to be done on the other.

Let's start by writing the inequality.

Subtract from both sides of the inequality.

Divide each side of the inequality by .

Solve.

The variable is greater than four.

### Example Question #1 : One Variable Equations

Solve for .

**Possible Answers:**

**Correct answer:**

In order to solve this problem we need isolate the variable on the left side o the equation. We will do this by performing the reverse of the operations that were done to the variable. It is important to note that what is done to one side of the equation needs to be done on the other.

Let's start by writing the equation.

Subtract from both sides of the equation.

Multiply both sides of the equation by .

Solve.

### Example Question #1 : Algebra

Solve for :

**Possible Answers:**

**Correct answer:**

Start by subtracting from both sides.

Next, add to both sides of the equation.

Finally, divide both sides by .

### Example Question #1 : One Variable Equations

Solve for :

**Possible Answers:**

**Correct answer:**

Start by subtracting both sides by .

Next, subtract both sides by .

Finally, divide both sides by .

### Example Question #1 : Linear Equations

What value of makes this a true statement?

**Possible Answers:**

**Correct answer:**

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on .

Multiplication precedes addition in the order of operations, so reverse the addition of 16 by subtracting 16 from both sides:

Now reverse multiplication by 2 by dividing by 2: