### All Algebra 1 Resources

## Example Questions

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality:

**Possible Answers:**

**Correct answer:**

In order to isolate the variable, we need to remove the coefficient. Since the operation between and is multiplication, we may want to divide both sides of the inequality by . Although this is a valid step, in order to simplify matters, instead of dividing by , we can multiplying by .

(Note: dividing by is exactly the same as multplying by the reciprocal, .)

Thus,

and after multiplying and simplifying, we obtain .

### Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Solve for :

**Possible Answers:**

None of the other answers

**Correct answer:**

Simplify by combining like terms to get .

Then, add and to both sides to separate the 's and intergers. This gives you .

Divide both sides to get . Since we didn't divide by a negative number, there is no need to reverse the sign.

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve for :

**Possible Answers:**

**Correct answer:**

Cross-cancel:

or, in interval form, .

### Example Question #1 : Equations / Inequalities

Solve for :

**Possible Answers:**

The inequality has no solution.

**Correct answer:**

Eliminate fractions by multiplying by the least common denominator - .

Cross-cancel:

### Example Question #5 : How To Find The Solution To An Inequality With Multiplication

Find the solution set for :

**Possible Answers:**

**Correct answer:**

Note the switch in inequality symbols when the numbers are multiplied by a negative number.

Cross-cancel:

or, in interval form,

### Example Question #1 : Equations / Inequalities

Solve for :

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

Subtract 4 from both sides. Then subtract 9x:

Next divide both sides by -6. Don't forget to switch the inequality because of the negative sign!

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve for :

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

To solve the inequality, subtract and add 12 to both sides to separate the from the integers:

Divide both sides by 2:

Note: The inequality sign is only flipped when dividing by negative numbers.

### Example Question #2 : Systems Of Inequalities

Solve for :

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

First, combine the like terms on the righthand side of the inequality to get .

Then, subtract and from both sides to get .

Finally, divide both sides by :

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve this inequality.

**Possible Answers:**

**Correct answer:**

Isolate all the terms with on one side and the other terms on the other side and solve for .

First subtract the an x from both sides of the inequality. The subtract 2 from each side. This results in the following inequality.

Here, we need to divide both sides by . However, whenever we divide or multiply and inequality by a negative number, we have to also change the direction of the inequality.

The final answer becomes

.

### Example Question #1 : Systems Of Inequalities

Find all of the solutions to this inequality.

**Possible Answers:**

**Correct answer:**

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by multiplying each side by two.

Whatever you do to one side you must also do to the other side.

This gives you:

The answer, therefore, is .

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