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Algebra 1 : Real Numbers

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Example Questions

Example Question #1 : How To Find Absolute Value

Simplify the following expression:

$\frac{14-\left | -16\right |}{60}$

Possible Answers:

$\frac{1}{2}$

$\frac{-1}{30}$

$\frac{-1}{15}$

Correct answer:

$\frac{-1}{30}$

Explanation:

Simplify the following expression:

$\frac{14-\left | -16\right |}{60}$

We can begin by changing the absolute value sign to a positive 16.

We can do this because negative numbers within an absolute value sign should always be thought of as positive numbers.

$\frac{14-16}{60}=\frac{-2}{60}$

Next, simplify your fraction to get

$\frac{-1}{30}$

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Example Question #11 : Number Lines And Absolute Value

Answer the following using $<, >, \leq, \geq, =$

$\left | -9 \right | \ \square \ 8$

Possible Answers:

$\geq$

$\leq$

Correct answer:

Explanation:

The absolute value of a number is equal to the distance that number is from zero on a number. Because it is a distance, it cannot be negative. So

$\left | -9\right |$

can be found at a distance of 9 from zero on a number. Therefore,

$\left | -9\right | = 9$

So, we can rewrite the original problem.

$9 \ \square \ 8$

This can now very easily be solved.

9 > 8

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Example Question #211 : Real Numbers

Solve: $\left | -3-36\right |$

Possible Answers:

Correct answer:

Explanation:

Solve what is inside the absolute value first.

$\left | -3-36\right | = \left | -39\right |$

Any value inside an absolute value will result to a positive number.

The answer is:

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Example Question #13 : Number Lines And Absolute Value

Solve: $-2\left | -3-4-5\right |$

Possible Answers:

Correct answer:

Explanation:

By order of operations, solve the terms inside the absolute value first.

-3-4-5 = -12

Any number inside an absolute value sign will be converted to positive.

$-2\left | -3-4-5\right | = -2(12)$

Multiply the two numbers.

The answer is:

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Example Question #212 : Real Numbers

Simplify the following:

$\left | 4-7 \right |$

Possible Answers:

Correct answer:

Explanation:

To solve, first treat the absolute value like a parenthesis and simplify your inside. Therefore you get,

$\left | 4-7 \right |=\left | -3 \right |$

Then, you must remember that absolute value means you make the quantity on the inside positive, so our number becomes 3 instead of negative 3.

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Example Question #15 : Number Lines And Absolute Value

Solve the following: $-2\left | -3-2\right |^2$

Possible Answers:

Correct answer:

Explanation:

Solve the terms inside of the absolute value first.

$-2\left | -3-2\right |^2=-2\left | -5\right |^2$

Simplify the inside of the absolute value. Any value inside will turn into a positive number.

-2(5)^2

Square the inner term.

-2(25)

Simplify.

The answer is:

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Example Question #16 : Number Lines And Absolute Value

Solve: $-2\left | 5\right |-2\left | -5\right |$

Possible Answers:

Correct answer:

Explanation:

Any value inside the absolute value signs will be converted to a positive number.

$-2\left | 5\right |-2\left | -5\right | = -2(5)-2(5)$

Distribute the terms and simplify.

-2(5)-2(5) = -10-10 = -20

The answer is:

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Example Question #213 : Real Numbers

Solve: $-\left | -2\right |-\left | -3\right |$

Possible Answers:

Correct answer:

Explanation:

Simplify all absolute values in the expression. The values inside the absolute values will be positive.

$-\left | -2\right |-\left | -3\right | = -(2)-(3)$

Subtract the numbers.

The answer is:

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Example Question #17 : How To Find Absolute Value

Possible Answers:

Correct answer:

Explanation:

Simplify the inner absolute value first. Any value inside an absolute value will be converted to positive.

Simplify the inner values of the first term and reduce the second term.

Subtract the numbers.

1-4 = -3

The answer is:

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Example Question #18 : How To Find Absolute Value

Solve the absolute value: $-2\left | -3-8\right |$

Possible Answers:

Correct answer:

Explanation:

Solve the parts inside the absolute value first.

$-2\left | -3-8\right | = -2 \left | -11\right |$

Any value inside the absolute value sign will be converted to a positive number.

Simplify the expression.

-2(11) =-22

The answer is:

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Algebra 1 : Real Numbers

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find Absolute Value

Example Question #11 : Number Lines And Absolute Value

Example Question #211 : Real Numbers

Example Question #13 : Number Lines And Absolute Value

Example Question #212 : Real Numbers

Example Question #15 : Number Lines And Absolute Value

Example Question #16 : Number Lines And Absolute Value

Example Question #213 : Real Numbers

Example Question #17 : How To Find Absolute Value

Example Question #18 : How To Find Absolute Value

All Algebra 1 Resources

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