QuestionSolve the equation $\frac{|-9+2 p|}{4}=2$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of an expression is the non-negative value of that expression without regard to its sign. . The equation is $\frac{|-9+ p|}{4}=$

STEP 2

First, we need to remove the fraction by multiplying both sides of the equation by4.
$4 \times \frac{|-9+2 p|}{4}=4 \times2$

STEP 3

implify the equation.
$|-9+2 p|=8$

STEP 4

The absolute value equation can be written as two separate equations. $-9+2 p=8$ and $-9+2 p=-8$

STEP 5

olve the first equation for p.
$-9+2 p=8 \Rightarrow2p=8+9 \Rightarrow2p=17 \Rightarrow p=\frac{17}{2}$

STEP 6

olve the second equation for p.
$-9+2 p=-8 \Rightarrow2p=-8+9 \Rightarrow2p=1 \Rightarrow p=\frac{1}{2}$ So, the solutions for the equation are $p=\frac{17}{2}$ and $p=\frac{1}{2}$ .

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QuestionSolve the equation $\frac{|-9+2 p|}{4}=2$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of an expression is the non-negative value of that expression without regard to its sign. . The equation is $\frac{|-9+ p|}{4}=$

STEP 2

First, we need to remove the fraction by multiplying both sides of the equation by4.
$4 \times \frac{|-9+2 p|}{4}=4 \times2$

STEP 3

implify the equation.
$|-9+2 p|=8$

STEP 4

The absolute value equation can be written as two separate equations. $-9+2 p=8$ and $-9+2 p=-8$

STEP 5

olve the first equation for p.
$-9+2 p=8 \Rightarrow2p=8+9 \Rightarrow2p=17 \Rightarrow p=\frac{17}{2}$

STEP 6

olve the second equation for p.
$-9+2 p=-8 \Rightarrow2p=-8+9 \Rightarrow2p=1 \Rightarrow p=\frac{1}{2}$ So, the solutions for the equation are $p=\frac{17}{2}$ and $p=\frac{1}{2}$ .

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QuestionSolve the equation ∣−9+2p∣4=2\frac{|-9+2 p|}{4}=24∣−9+2p∣​=2.

Studdy Solution

STEP 1

Assumptions1. The absolute value of an expression is the non-negative value of that expression without regard to its sign. . The equation is ∣−9+p∣4=\frac{|-9+ p|}{4}=4∣−9+p∣​=

STEP 2

First, we need to remove the fraction by multiplying both sides of the equation by4.4×∣−9+2p∣4=4×24 \times \frac{|-9+2 p|}{4}=4 \times24×4∣−9+2p∣​=4×2

STEP 3

implify the equation.∣−9+2p∣=8|-9+2 p|=8∣−9+2p∣=8

STEP 4

The absolute value equation can be written as two separate equations.−9+2p=8-9+2 p=8−9+2p=8and−9+2p=−8-9+2 p=-8−9+2p=−8

STEP 5

olve the first equation for p.−9+2p=8⇒2p=8+9⇒2p=17⇒p=172-9+2 p=8 \Rightarrow2p=8+9 \Rightarrow2p=17 \Rightarrow p=\frac{17}{2}−9+2p=8⇒2p=8+9⇒2p=17⇒p=217​

STEP 6

olve the second equation for p.−9+2p=−8⇒2p=−8+9⇒2p=1⇒p=12-9+2 p=-8 \Rightarrow2p=-8+9 \Rightarrow2p=1 \Rightarrow p=\frac{1}{2}−9+2p=−8⇒2p=−8+9⇒2p=1⇒p=21​So, the solutions for the equation are p=172p=\frac{17}{2}p=217​ and p=12p=\frac{1}{2}p=21​.

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QuestionSolve the equation $\frac{|-9+2 p|}{4}=2$ .

Assumptions1. The absolute value of an expression is the non-negative value of that expression without regard to its sign. . The equation is $\frac{|-9+ p|}{4}=$

First, we need to remove the fraction by multiplying both sides of the equation by4.
$4 \times \frac{|-9+2 p|}{4}=4 \times2$

implify the equation.
$|-9+2 p|=8$

The absolute value equation can be written as two separate equations. $-9+2 p=8$ and $-9+2 p=-8$

olve the first equation for p.
$-9+2 p=8 \Rightarrow2p=8+9 \Rightarrow2p=17 \Rightarrow p=\frac{17}{2}$

olve the second equation for p.
$-9+2 p=-8 \Rightarrow2p=-8+9 \Rightarrow2p=1 \Rightarrow p=\frac{1}{2}$ So, the solutions for the equation are $p=\frac{17}{2}$ and $p=\frac{1}{2}$ .