Solved on Sep 15, 2023

Solve for $n$ given $-|n|=-2$ . Write the solution as an integer or simplified fraction.

STEP 1

Assumptions1. The absolute value of a number is always non-negative. This means that $|n|$ is always greater than or equal to0. . We are solving for $n$ in the equation $-|n|=-$ .

STEP 2

The equation given is $-|n|=-2$ . Since the absolute value of a number is always non-negative, the negative of an absolute value will always be non-positive. This means that $-|n|$ is always less than or equal to0.

STEP 3

However, in the equation $-|n|=-2$ , the right side of the equation is -2, which is less than0. This means that there are possible values for $n$ that will satisfy the equation.

STEP 4

To solve for $n$ , we need to get rid of the negative sign on the left side of the equation. We can do this by multiplying both sides of the equation by -1.
$-1 \times -|n| = -1 \times -2$

STEP 5

This simplifies to $|n| =2$

STEP 6

The absolute value of a number is the distance of that number from0 on the number line. This means that if $|n| =2$ , then $n$ is2 units away from0 on the number line. This gives us two possible values for $n$ :2 and -2.
So, the solutions to the equation are $n =2$ and $n = -2$ .

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Solve for $n$ given $-|n|=-2$ . Write the solution as an integer or simplified fraction.

STEP 1

Assumptions1. The absolute value of a number is always non-negative. This means that $|n|$ is always greater than or equal to0. . We are solving for $n$ in the equation $-|n|=-$ .

STEP 2

The equation given is $-|n|=-2$ . Since the absolute value of a number is always non-negative, the negative of an absolute value will always be non-positive. This means that $-|n|$ is always less than or equal to0.

STEP 3

However, in the equation $-|n|=-2$ , the right side of the equation is -2, which is less than0. This means that there are possible values for $n$ that will satisfy the equation.

STEP 4

To solve for $n$ , we need to get rid of the negative sign on the left side of the equation. We can do this by multiplying both sides of the equation by -1.
$-1 \times -|n| = -1 \times -2$

STEP 5

This simplifies to $|n| =2$

STEP 6

The absolute value of a number is the distance of that number from0 on the number line. This means that if $|n| =2$ , then $n$ is2 units away from0 on the number line. This gives us two possible values for $n$ :2 and -2.
So, the solutions to the equation are $n =2$ and $n = -2$ .

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Solve for nnn given −∣n∣=−2-|n|=-2−∣n∣=−2. Write the solution as an integer or simplified fraction.

STEP 1

Assumptions1. The absolute value of a number is always non-negative. This means that ∣n∣|n|∣n∣ is always greater than or equal to0. . We are solving for nnn in the equation −∣n∣=−-|n|=-−∣n∣=−.

STEP 2

The equation given is −∣n∣=−2-|n|=-2−∣n∣=−2. Since the absolute value of a number is always non-negative, the negative of an absolute value will always be non-positive. This means that −∣n∣-|n|−∣n∣ is always less than or equal to0.

STEP 3

However, in the equation −∣n∣=−2-|n|=-2−∣n∣=−2, the right side of the equation is -2, which is less than0. This means that there are possible values for nnn that will satisfy the equation.

STEP 4

To solve for nnn, we need to get rid of the negative sign on the left side of the equation. We can do this by multiplying both sides of the equation by -1.−1×−∣n∣=−1×−2-1 \times -|n| = -1 \times -2−1×−∣n∣=−1×−2

STEP 5

This simplifies to∣n∣=2|n| =2∣n∣=2

STEP 6

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Solve for $n$ given $-|n|=-2$ . Write the solution as an integer or simplified fraction.

Assumptions1. The absolute value of a number is always non-negative. This means that $|n|$ is always greater than or equal to0. . We are solving for $n$ in the equation $-|n|=-$ .

The equation given is $-|n|=-2$ . Since the absolute value of a number is always non-negative, the negative of an absolute value will always be non-positive. This means that $-|n|$ is always less than or equal to0.

However, in the equation $-|n|=-2$ , the right side of the equation is -2, which is less than0. This means that there are possible values for $n$ that will satisfy the equation.

To solve for $n$ , we need to get rid of the negative sign on the left side of the equation. We can do this by multiplying both sides of the equation by -1.
$-1 \times -|n| = -1 \times -2$

This simplifies to $|n| =2$