Number Lines and Absolute Value - Algebra

Card 0 of 297

Question

Solve for .

$-3\left | p+2 \right |=-12$

Answer

Divide both sides by .

$\frac{-3\left | p+2 \right |}{-3}=\frac{-12}{-3}$

$\left | p+2 \right |=4$

Remove the absolute value brackets by setting the expression equal to both the positive and negative values of 4:

or

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Question

Evaluate the expression.

$\small 3(\frac{(8-10)^2}{\left | 8-10 \right |})$

Answer

$\small 3(\frac{(8-10)^2}{\left | 8-10 \right |})$

First, simplify the terms in parentheses and absolute value.

$3(\frac{-2^2}{\left | -2 \right |})$

Remember that the absolute value of a negative term is positive.

$3(\frac{4}{2})$

Multiply and simplify.

$\frac{3*4}{2}=\frac{12}{2}=6$

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Question

What number or numbers have absolute value ?

Answer

The absolute value of every real number is nonnegative, so no number with absolute value can exist.

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Question

What number or numbers have absolute value ?

Answer

The absolute value of every real number is nonnegative, so no number with absolute value can exist.

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Question

What number or numbers have absolute value 29?

Answer

The absolute value of any positive number is the number itself, so 29 has 29 as an absolute value. Also, the absolute value of a negative number is its (positive) opposite, so also has 29 as an absolute value.

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Question

What number or numbers have absolute value 11?

Answer

The absolute value of any positive number is the number itself, so 11 has 11 as an absolute value. Also, the absolute value of a negative number is its (positive) opposite, so also has 11 as an absolute value.

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Question

Mr. Smith and his wife went on a trip, they travelled miles towards their destination, however on the way there they had to turn around and drive miles away from their destination to get Mr. Smith's wallet from the store. After getting his wallet they drove more miles to reach their destination. What is the total number of miles that the family covered?

Answer

Even though the Smiths travelled backwards you still have to add the positive number to the equation. So it looks like this:

$\left | 25\right |+\left | -5\right |+\left |20 \right |= 25+5+20$ which equals

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Question

Simplify the following equation:

$\left | -9\right |-\left | 4\right |$

Answer

It is important to understand that the absolute value is the distance from a number is.

To simply this equation you need to simplify the absolute values first.

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

$\left | 4\right |=4$

Then simplify the function

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Question

Solve: $\left | x+3\right | = 5$

Answer

In order to solve this absolute value, we will need to split up the absolute value in its positive and negative solution.

Break up the absolute value and rewrite the terms for the positive solution and solve for .

For the negative solution, split up the absolute value and add a negative in front of the quantity which was contained by the absolute value.

Divide by negative one on both sides.

Subtract three on both sides.

Simplify both sides.

The answers to this question are:

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Question

Simplify:

$\left | -2*4+14\right |$

Answer

First simplify the inside of the absolute value, remembering PEMDAS is important here.

So first you multiply and then add the fourteen.

So:

$\left |-8+14 \right |$ $=\left | 6\right |=6$

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Question

Simplify the following expression:

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

Answer

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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Question

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

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

Answer

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.

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Question

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

Answer

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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Question

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

Answer

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

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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Question

Simplify the following:

$\left | 4-7 \right |$

Answer

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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Question

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

Answer

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.

Square the inner term.

Simplify.

The answer is:

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Question

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

Answer

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.

The answer is:

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Question

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

Answer

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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Question

Solve the absolute values: $\left | -2+\left | -3\right |\right |-\left | -4\right |$

Answer

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

$\left | -2+\left | -3\right |\right |-\left | -4\right | = \left | -2+3|-\left | -4\right |$

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

$\left | -2+3|-\left | -4\right | = \left | 1\right |-(4)$

Subtract the numbers.

The answer is:

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Question

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

Answer

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.

The answer is:

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