QuestionSolve the inequality $5|p+1|<10$ and express the solution in interval notation using decimals.

Studdy Solution

STEP 1

Assumptions1. The absolute value inequality is $5|p+1|<10$ . . We need to solve this inequality and express the answer in interval notation.
3. Decimal form should be used for numerical values.

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the inequality by5.
$|p+1|<\frac{10}{5}$

STEP 3

Now, simplify the right side of the inequality.
$|p+1|<2$

STEP 4

The absolute value inequality $|p+1|<2$ can be rewritten as a compound inequality without absolute values $-2<p+1<2$ .

STEP 5

To isolate $p$ , we subtract1 from all parts of the inequality.
$-2-1<p+1-1<2-1$

STEP 6

implify the inequality to get the solution.
$-3<p<1$ This is the solution to the inequality in interval notation $(-3,1)$ .

Was this helpful?

QuestionSolve the inequality $5|p+1|<10$ and express the solution in interval notation using decimals.

Studdy Solution

STEP 1

Assumptions1. The absolute value inequality is $5|p+1|<10$ . . We need to solve this inequality and express the answer in interval notation.
3. Decimal form should be used for numerical values.

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the inequality by5.
$|p+1|<\frac{10}{5}$

STEP 3

Now, simplify the right side of the inequality.
$|p+1|<2$

STEP 4

The absolute value inequality $|p+1|<2$ can be rewritten as a compound inequality without absolute values $-2<p+1<2$ .

STEP 5

To isolate $p$ , we subtract1 from all parts of the inequality.
$-2-1<p+1-1<2-1$

STEP 6

implify the inequality to get the solution.
$-3<p<1$ This is the solution to the inequality in interval notation $(-3,1)$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality 5∣p+1∣<105|p+1|<105∣p+1∣<10 and express the solution in interval notation using decimals.

Studdy Solution

STEP 1

Assumptions1. The absolute value inequality is 5∣p+1∣<105|p+1|<105∣p+1∣<10. . We need to solve this inequality and express the answer in interval notation.3. Decimal form should be used for numerical values.

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the inequality by5.∣p+1∣<105|p+1|<\frac{10}{5}∣p+1∣<510​

STEP 3

Now, simplify the right side of the inequality.∣p+1∣<2|p+1|<2∣p+1∣<2

STEP 4

The absolute value inequality ∣p+1∣<2|p+1|<2∣p+1∣<2 can be rewritten as a compound inequality without absolute values −2<p+1<2-2<p+1<2−2<p+1<2.

STEP 5

To isolate ppp, we subtract1 from all parts of the inequality.−2−1<p+1−1<2−1-2-1<p+1-1<2-1−2−1<p+1−1<2−1

STEP 6

implify the inequality to get the solution.−3<p<1-3<p<1−3<p<1This is the solution to the inequality in interval notation (−3,1)(-3,1)(−3,1).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality $5|p+1|<10$ and express the solution in interval notation using decimals.

Assumptions1. The absolute value inequality is $5|p+1|<10$ . . We need to solve this inequality and express the answer in interval notation.
3. Decimal form should be used for numerical values.

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the inequality by5.
$|p+1|<\frac{10}{5}$

Now, simplify the right side of the inequality.
$|p+1|<2$

The absolute value inequality $|p+1|<2$ can be rewritten as a compound inequality without absolute values $-2<p+1<2$ .

To isolate $p$ , we subtract1 from all parts of the inequality.
$-2-1<p+1-1<2-1$

implify the inequality to get the solution.
$-3<p<1$ This is the solution to the inequality in interval notation $(-3,1)$ .