Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #61 : Systems Of Inequalities

Solve this inequality:

Possible Answers:

Not enough information to be determined.

Correct answer:

Explanation:

To solve this inequality, we need to separate the constants from the variables so that they are on opposite sides of the inequality.

We can do this by adding (4x+5) to each side and  

.

The constants cancel on the left side, and the variables cancel on the right side.

 

Then, we divide both sides by 16, to get our final answer:

Example Question #62 : Systems Of Inequalities

Simplify the following inequality:

Possible Answers:

Correct answer:

Explanation:

This is a one-step problem in which all you need to do is add the  to both sides to get  by itself.

So, 

Then simplify to get: 

Example Question #63 : Systems Of Inequalities

Find all of the solutions to this inequality.

Possible Answers:

Correct answer:

Explanation:

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 subtracting three from each side.

Whatever operation you do to one side you must do to the other side as well.

This gives you:

The answer, therefore, is .

Example Question #64 : Systems Of Inequalities

Solve the inequality:  

Possible Answers:

Correct answer:

Explanation:

In order to isolate the  variable, we will need to add nine on both sides.

Simplify both sides of the equation.

The answer is .

Example Question #65 : Systems Of Inequalities

Solve the following inequality:  

Possible Answers:

Correct answer:

Explanation:

Add both sides by four to isolate the  variable.

Simplify both sides of the equation.

The answer is:  

This means that  is greater than forty, but cannot equal to forty.

Example Question #66 : Systems Of Inequalities

Solve for x in the following inequality:

Possible Answers:

Correct answer:

Explanation:

When solving an inequality, we will solve it the same way we would solve an equation.  We are solving for x, so we want x to stand alone. In the equation

we want to add 5 to both sides. The inequality symbol does not change.  We get

Example Question #67 : Systems Of Inequalities

Find the solution of the inequality:  

Possible Answers:

Correct answer:

Explanation:

To isolate the unknown variable, we will need to add 14 on both sides.

Simplify both sides of the equation.

The answer is:  

Example Question #68 : Systems Of Inequalities

Solve the inequality:  

Possible Answers:

Correct answer:

Explanation:

In order to solve for the unknown variable, add 12 on both sides.

Simplify both sides.

The answer is:  

Example Question #69 : Systems Of Inequalities

Find the solution:    

Possible Answers:

Correct answer:

Explanation:

To solve this inequality, simply add the variable on both sides.  This method eliminates having to divide by negative one on both sides and switch the sign.

This inequality is the same as   since the unknown variable must be greater than three.

Example Question #70 : Systems Of Inequalities

Solve the following inequality:  

Possible Answers:

Correct answer:

Explanation:

In order to solve this inequality, we must add six and three on both sides of the inequality to isolate the x-variable.

This will cancel out the terms and leave x by itself on the left side.

The answer is:  

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