Question Solve the absolute value equation $2|4x+5| = 0$ and choose the correct solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is $|4x+5|=0$ . The absolute value of a number is always non-negative, that is, it is either positive or zero.
3. The equation is in the form $a|bx+c|=0$ , where $a$ , $b$ , and $c$ are constants.

STEP 2

First, we need to understand that the absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of a number can never be negative.

STEP 3

Since the absolute value of a number can never be negative, the only way for $2|x+5|$ to be equal to zero is if $|x+5|$ itself is zero. $2|x+5|=0 \implies |x+5|=0$

STEP 4

The absolute value of a number is zero if and only if the number itself is zero. Therefore, we can set the expression inside the absolute value equal to zero.
$4x+=0$

STEP 5

Now, we can solve the equation for $x$ by first subtracting $5$ from both sides.
$4x+5-5=0-5$

STEP 6

implify the equation.
$4x=-5$

STEP 7

Finally, we can solve for $x$ by dividing both sides by $4$ .
$x=-\frac{5}{4}$ So, the solution to the equation $2|4x+5|=0$ is $x=-\frac{5}{4}$ .

Was this helpful?

Question Solve the absolute value equation $2|4x+5| = 0$ and choose the correct solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is $|4x+5|=0$ . The absolute value of a number is always non-negative, that is, it is either positive or zero.
3. The equation is in the form $a|bx+c|=0$ , where $a$ , $b$ , and $c$ are constants.

STEP 2

First, we need to understand that the absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of a number can never be negative.

STEP 3

Since the absolute value of a number can never be negative, the only way for $2|x+5|$ to be equal to zero is if $|x+5|$ itself is zero. $2|x+5|=0 \implies |x+5|=0$

STEP 4

The absolute value of a number is zero if and only if the number itself is zero. Therefore, we can set the expression inside the absolute value equal to zero.
$4x+=0$

STEP 5

Now, we can solve the equation for $x$ by first subtracting $5$ from both sides.
$4x+5-5=0-5$

STEP 6

implify the equation.
$4x=-5$

STEP 7

Finally, we can solve for $x$ by dividing both sides by $4$ .
$x=-\frac{5}{4}$ So, the solution to the equation $2|4x+5|=0$ is $x=-\frac{5}{4}$ .

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.

Question Solve the absolute value equation 2∣4x+5∣=02|4x+5| = 02∣4x+5∣=0 and choose the correct solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is ∣4x+5∣=0|4x+5|=0∣4x+5∣=0 . The absolute value of a number is always non-negative, that is, it is either positive or zero.3. The equation is in the form a∣bx+c∣=0a|bx+c|=0a∣bx+c∣=0, where aaa, bbb, and ccc are constants.

STEP 2

First, we need to understand that the absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of a number can never be negative.

STEP 3

Since the absolute value of a number can never be negative, the only way for 2∣x+5∣2|x+5|2∣x+5∣ to be equal to zero is if ∣x+5∣|x+5|∣x+5∣ itself is zero.2∣x+5∣=0 ⟹ ∣x+5∣=02|x+5|=0 \implies |x+5|=02∣x+5∣=0⟹∣x+5∣=0

STEP 4

The absolute value of a number is zero if and only if the number itself is zero. Therefore, we can set the expression inside the absolute value equal to zero.4x+=04x+=04x+=0

STEP 5

Now, we can solve the equation for xxx by first subtracting 555 from both sides.4x+5−5=0−54x+5-5=0-54x+5−5=0−5

STEP 6

implify the equation.4x=−54x=-54x=−5

STEP 7

Finally, we can solve for xxx by dividing both sides by 444.x=−54x=-\frac{5}{4}x=−45​So, the solution to the equation 2∣4x+5∣=02|4x+5|=02∣4x+5∣=0 is x=−54x=-\frac{5}{4}x=−45​.

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.

Question Solve the absolute value equation $2|4x+5| = 0$ and choose the correct solution.

Assumptions1. The given equation is $|4x+5|=0$ . The absolute value of a number is always non-negative, that is, it is either positive or zero.
3. The equation is in the form $a|bx+c|=0$ , where $a$ , $b$ , and $c$ are constants.

Since the absolute value of a number can never be negative, the only way for $2|x+5|$ to be equal to zero is if $|x+5|$ itself is zero. $2|x+5|=0 \implies |x+5|=0$

The absolute value of a number is zero if and only if the number itself is zero. Therefore, we can set the expression inside the absolute value equal to zero.
$4x+=0$

Now, we can solve the equation for $x$ by first subtracting $5$ from both sides.
$4x+5-5=0-5$

implify the equation.
$4x=-5$

Finally, we can solve for $x$ by dividing both sides by $4$ .
$x=-\frac{5}{4}$ So, the solution to the equation $2|4x+5|=0$ is $x=-\frac{5}{4}$ .