Math / Algebra

Question $|x-2|<3$

Studdy Solution

STEP 1

What is this asking? This is asking us to find all the numbers $x$ whose distance from $2$ is less than $3$ . Watch out! Remember that absolute value represents distance, and distances are always non-negative!

STEP 2

1. Rewrite the inequality without absolute value.
2. Isolate $x$ .

STEP 3

The absolute value of a number is its distance from zero.
So $|x-2|$ means the distance between $x$ and $2$ .
We're told this distance is less than $3$ .

STEP 4

This means $x$ is trapped between $2-3$ and $2+3$ .
Mathematically, we write this as: $2 - 3 < x < 2 + 3$

STEP 5

Let's simplify those numbers! $2 - 3$ is $-1$ and $2 + 3$ is $5$ .
So our inequality becomes: $-1 < x < 5$

STEP 6

This tells us $x$ can be any number between $-1$ and $5$ , but not including $-1$ or $5$ .

STEP 7

All $x$ values such that $-1 < x < 5$ satisfy the original inequality.
We can also write this using interval notation as $(-1, 5)$ .

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Question $|x-2|<3$

Studdy Solution

STEP 1

What is this asking? This is asking us to find all the numbers $x$ whose distance from $2$ is less than $3$ . Watch out! Remember that absolute value represents distance, and distances are always non-negative!

STEP 2

1. Rewrite the inequality without absolute value.
2. Isolate $x$ .

STEP 3

The absolute value of a number is its distance from zero.
So $|x-2|$ means the distance between $x$ and $2$ .
We're told this distance is less than $3$ .

STEP 4

This means $x$ is trapped between $2-3$ and $2+3$ .
Mathematically, we write this as: $2 - 3 < x < 2 + 3$

STEP 5

Let's simplify those numbers! $2 - 3$ is $-1$ and $2 + 3$ is $5$ .
So our inequality becomes: $-1 < x < 5$

STEP 6

This tells us $x$ can be any number between $-1$ and $5$ , but not including $-1$ or $5$ .

STEP 7

All $x$ values such that $-1 < x < 5$ satisfy the original inequality.
We can also write this using interval notation as $(-1, 5)$ .

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Question∣x−2∣<3|x-2|<3∣x−2∣<3

Studdy Solution

STEP 1

What is this asking? This is asking us to find all the numbers xxx whose distance from 222 is less than 333. Watch out! Remember that absolute value represents distance, and distances are always non-negative!

STEP 2

1. Rewrite the inequality without absolute value.2. Isolate xxx.

STEP 3

The absolute value of a number is its distance from zero.So ∣x−2∣|x-2|∣x−2∣ means the distance between xxx and 222.We're told this distance is less than 333.

STEP 4

This means xxx is trapped between 2−32-32−3 and 2+32+32+3.Mathematically, we write this as: 2−3<x<2+32 - 3 < x < 2 + 32−3<x<2+3

STEP 5

Let's simplify those numbers! 2−32 - 32−3 is −1-1−1 and 2+32 + 32+3 is 555.So our inequality becomes: −1<x<5-1 < x < 5−1<x<5

STEP 6

This tells us xxx can be any number between −1-1−1 and 555, but *not* including −1-1−1 or 555.

STEP 7

All xxx values such that −1<x<5-1 < x < 5−1<x<5 satisfy the original inequality.We can also write this using interval notation as (−1,5)(-1, 5)(−1,5).

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Question $|x-2|<3$

What is this asking? This is asking us to find all the numbers $x$ whose distance from $2$ is less than $3$ . Watch out! Remember that absolute value represents distance, and distances are always non-negative!

1. Rewrite the inequality without absolute value.
2. Isolate $x$ .

The absolute value of a number is its distance from zero.
So $|x-2|$ means the distance between $x$ and $2$ .
We're told this distance is less than $3$ .

This means $x$ is trapped between $2-3$ and $2+3$ .
Mathematically, we write this as: $2 - 3 < x < 2 + 3$

Let's simplify those numbers! $2 - 3$ is $-1$ and $2 + 3$ is $5$ .
So our inequality becomes: $-1 < x < 5$

This tells us $x$ can be any number between $-1$ and $5$ , but not including $-1$ or $5$ .

All $x$ values such that $-1 < x < 5$ satisfy the original inequality.
We can also write this using interval notation as $(-1, 5)$ .