Algebra 1 : Linear Inequalities

Example Questions

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Example Question #1 : Writing Inequalities

Write a compound inequality that describes the given graph:

Explanation:

The graph shows an arrow beginning on 5 with an open circle and pointing to the left, thus that portion of the graph says, all real numbers less than 5. There is a second arrow beginning on 9 with a closed circle and pointing to the right, representing all real numbers greater than or equal to 9. Since we are joining the two parts of the graph, we have a compound inequality utilizing the "or" statement. So our answer is .

Example Question #1 : Writing Inequalities

Write as an algebraic inequality:

Twenty subtracted from the product of seven and a number exceeds one hundred.

Explanation:

"The product of seven and a number " is . "Twenty subtracted from the product of seven and a number" is  . "Exceeds one hundred" means that this is greater than one hundred, so the correct inequality is

Example Question #3 : Writing Inequalities

Write as an algebraic inequality:

Twice the sum of a number and sixteen is no less than sixty.

Explanation:

"The sum of a number and sixteen" is translates to ; twice that sum is . " Is no less than sixty" means that this is greater than or equal to sixty, so the desired inequality is

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Example Question #1 : Writing Inequalities

Write as an algebraic inequality:

Twice the sum of a number and sixteen does not exceed eighty.

Explanation:

"The sum of a number and sixteen" translates to ; twice that sum is . "Does not exceed eighty" means that it is less than or equal to eighty, so the desired inequality is

Example Question #5 : Writing Inequalities

A candy company is inspecting its factory. In a standard bag of candy there are a minimum of 14 individual candies, and a maximum of 22. Let  be the number of candies in a standard bag. Write an expression for  using inequalities.

Explanation:

In terms of inequalities, we know two things.  is greater than or equal to 14 (which is the same as  being greater than 13). And we know  is less than or equal to 22 (which is the same as  being less than 23).

So, we have to find the correct statement where we can find the two inequalities. We see we need    and .

Therefore the only answer that fits our needs is .

Example Question #6 : Writing Inequalities

Write an inequality that represents the following number line.

Explanation:

On the number line, the graph starts at –1 and ends at 3.

The line runs between –1 and 3, so we know our inequality involves only values of x that fall between these two numbers. The open circle at –1 indicates that –1 is not included, while the shaded circle on 3 indicates that 3 is included.

Combining these two inequalities into one give us our answer.

Example Question #7 : Writing Inequalities

Find the solution set of the inequality:

Explanation:

or, in interval notation,

Example Question #8 : Writing Inequalities

Find the solution set of the inequality:

Explanation:

or, in interval notation,

Example Question #9 : Writing Inequalities

Solve for :

Explanation:

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

Then subtract  from both sides of the inequality:

Next, subtract the 12:

Finally, divide by two:

Example Question #10 : Writing Inequalities

Solve the inequality.