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Algebra 1 : Linear Inequalities

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Example Questions

Example Question #1 : Writing Inequalities

Write a compound inequality that describes the given graph: Or_open

Possible Answers:

$\small x<5 \quad or \quad x \ge 9$

$\small x > 5 \quad or \quad x \le 9$

$\small x \le 5 \quad or \quad x > 9$

$\small x < 5 \quad and \quad x \ge 9$

$\small x > 5 \quad and \quad x \le 9$

Correct answer:

$\small x<5 \quad or \quad x \ge 9$

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 $\small x<5 \quad or \quad x \ge 9$ .

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Example Question #1 : Writing Inequalities

Write as an algebraic inequality:

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

Possible Answers:

$7x - 20 \geq 100$

$20-7x \geq 100$

7x - 20 > 100

20-7x > 100

7(x-20) > 100

Correct answer:

7x - 20 > 100

Explanation:

"The product of seven and a number " is . "Twenty subtracted from the product of seven and a number" is 7x - 20 . "Exceeds one hundred" means that this is greater than one hundred, so the correct inequality is

7x - 20 > 100

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Example Question #2 : Writing Inequalities

Write as an algebraic inequality:

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

Possible Answers:

$2 (x+16) \neq 60$

2 (x+16) > 60

$2x+16 \geq 60$

2x+16 > 60

$2 (x+16) \geq 60$

Correct answer:

$2 (x+16) \geq 60$

Explanation:

"The sum of a number and sixteen" is translates to x + 16 ; twice that sum is 2(x+16) . " Is no less than sixty" means that this is greater than or equal to sixty, so the desired inequality is

$2(x+16) \geq 60$ .

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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.

Possible Answers:

$2x+16 \geq 80$

$2x+16 \leq 80$

2x+16 > 80

2 (x+16) < 80

$2 (x+16) \leq 80$

Correct answer:

$2 (x+16) \leq 80$

Explanation:

"The sum of a number and sixteen" translates to x + 16 ; twice that sum is 2 (x+16) . "Does not exceed eighty" means that it is less than or equal to eighty, so the desired inequality is

$2 (x+16) \leq 80$

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Example Question #1 : 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.

Possible Answers:

$14\geq x\geq 22$

$14\leq x\geq 22$

13< x> 23

14< x< 22

$13< x\leq 22$

Correct answer:

$13< x\leq 22$

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 $14\leq x \text{ or } 13< x$ and $x\leq 22 \text{ or }x< 23$ .

Therefore the only answer that fits our needs is $13< x\leq 22$ .

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Example Question #1 : Writing Inequalities

Write an inequality that represents the following number line.

Possible Answers:

$1\leq x\leq 3$

x>3 , x<-1

$-1\leq x< 3$

$-1<x\leq3$

$3<x\leq-1$

Correct answer:

$-1<x\leq3$

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.

x>-1

$x\leq3$

Combining these two inequalities into one give us our answer.

$-1<x\leq3$

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Example Question #3 : Writing Inequalities

Find the solution set of the inequality:

$6x + 22 \leq 97$

Possible Answers:

$(-\infty , -12.5]$

$[12.5, \infty)$

$\left ( -\infty , \infty \right )$

$[-12.5, \infty)$

$(-\infty , 12.5]$

Correct answer:

$(-\infty , 12.5]$

Explanation:

$6x + 22 \leq 97$

$6x + 22 -22 \leq 97-22$

$6x \leq 75$

$6x \div 6 \leq 75\div 6$

$x \leq 12.5$

or, in interval notation, $(-\infty , 12.5]$

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Example Question #1 : Writing Inequalities

Find the solution set of the inequality:

6x + 22 > 67

Possible Answers:

$\left ( -7.5, \infty \right )$

$\left ( 7.5, \infty \right )$

$\left ( - \infty, -7.5 \right )$

$\left ( -\infty , \infty \right )$

$\left ( - \infty, 7.5 \right )$

Correct answer:

$\left ( 7.5, \infty \right )$

Explanation:

6x + 22 > 67

6x + 22 -22 > 67 -22

6x > 45

$6x \div 6 > 45\div 6$

x > 7.5

or, in interval notation, $\left ( 7.5, \infty \right )$

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Example Question #1 : Writing Inequalities

Solve for :

$3(x + 4) \leq x - 6$

Possible Answers:

$x \leq -9$

$x \geq -9$

$x \geq 9$

$x \leq 3$

$x \leq 9$

Correct answer:

$x \leq -9$

Explanation:

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

$3(x + 4) \leq x - 6$

$3x + 12 \leq x - 6$

Then subtract from both sides of the inequality:

$2x + 12 \leq -6$

Next, subtract the 12:

$2x \leq -18$

Finally, divide by two:

$x \leq -9$

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Example Question #1 : Writing Inequalities

Solve the inequality. $3x-4\leq 12x+16$

Possible Answers:

$x\geq -\frac{4}{3}$

$x\leq -\frac{4}{3}$

$x\leq -\frac{20}{9}$

$x\geq \frac{20}{9}$

$x\geq -\frac{20}{9}$

Correct answer:

$x\geq -\frac{20}{9}$

Explanation:

To solve $3x-4\leq 12x+16$ , it is necessary to isolate the variable and the integers.

Subtract and from both sides of the equation.

$-20\leq 9x$

Divide by nine on both sides.

$-\frac{20}{9}\leq x$

This answer is also the same as: $x\geq -\frac{20}{9}$

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Algebra 1 : Linear Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #2 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #3 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

Example Question #1 : Writing Inequalities

All Algebra 1 Resources

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