Solved on Sep 26, 2023

Solve the equation $|4 x-1|=6$ for $x$ .

STEP 1

Assumptions1. The equation is $|4x -1| =6$ . We need to find the equivalent equations without the absolute value

STEP 2

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|a| = b$ has two solutions $a = b$ and $a = -b$ . We can apply this concept to our equation.

STEP 3

Applying this concept to our equation, we get two equations1. $x -1 =6$
2. $x -1 = -6$

STEP 4

Now, we solve the first equation for $x$ .
$4x -1 =6$

STEP 5

Add1 to both sides of the equation to isolate $4x$ on one side.
$4x = +1$

STEP 6

Calculate the right side of the equation.
$4x =$

STEP 7

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{7}{4}$

STEP 8

Now, we solve the second equation for $x$ .
$4x -1 = -6$

STEP 9

Add to both sides of the equation to isolate $4x$ on one side.
$4x = -6 +$

STEP 10

Calculate the right side of the equation.
$4x = -5$

STEP 11

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{-5}{4}$ The equation $|4x -| =6$ is equivalent to $x = \frac{7}{4}$ or $x = \frac{-5}{4}$ .

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Solve the equation $|4 x-1|=6$ for $x$ .

STEP 1

Assumptions1. The equation is $|4x -1| =6$ . We need to find the equivalent equations without the absolute value

STEP 2

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|a| = b$ has two solutions $a = b$ and $a = -b$ . We can apply this concept to our equation.

STEP 3

Applying this concept to our equation, we get two equations1. $x -1 =6$
2. $x -1 = -6$

STEP 4

Now, we solve the first equation for $x$ .
$4x -1 =6$

STEP 5

Add1 to both sides of the equation to isolate $4x$ on one side.
$4x = +1$

STEP 6

Calculate the right side of the equation.
$4x =$

STEP 7

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{7}{4}$

STEP 8

Now, we solve the second equation for $x$ .
$4x -1 = -6$

STEP 9

Add to both sides of the equation to isolate $4x$ on one side.
$4x = -6 +$

STEP 10

Calculate the right side of the equation.
$4x = -5$

STEP 11

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{-5}{4}$ The equation $|4x -| =6$ is equivalent to $x = \frac{7}{4}$ or $x = \frac{-5}{4}$ .

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Solve the equation ∣4x−1∣=6|4 x-1|=6∣4x−1∣=6 for xxx.

STEP 1

Assumptions1. The equation is ∣4x−1∣=6|4x -1| =6∣4x−1∣=6 . We need to find the equivalent equations without the absolute value

STEP 2

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, ∣a∣=b|a| = b∣a∣=b has two solutions a=ba = ba=b and a=−ba = -ba=−b. We can apply this concept to our equation.

STEP 3

Applying this concept to our equation, we get two equations1. x−1=6x -1 =6x−1=62. x−1=−6x -1 = -6x−1=−6

STEP 4

Now, we solve the first equation for xxx.4x−1=64x -1 =64x−1=6

STEP 5

Add1 to both sides of the equation to isolate 4x4x4x on one side.4x=+14x = +14x=+1

STEP 6

Calculate the right side of the equation.4x=4x =4x=

STEP 7

Divide both sides of the equation by4 to solve for xxx.x=74x = \frac{7}{4}x=47​

STEP 8

Now, we solve the second equation for xxx.4x−1=−64x -1 = -64x−1=−6

STEP 9

Add to both sides of the equation to isolate 4x4x4x on one side.4x=−6+4x = -6 +4x=−6+

STEP 10

Calculate the right side of the equation.4x=−54x = -54x=−5

STEP 11

Divide both sides of the equation by4 to solve for xxx.x=−54x = \frac{-5}{4}x=4−5​The equation ∣4x−∣=6|4x -| =6∣4x−∣=6 is equivalent to x=74x = \frac{7}{4}x=47​ or x=−54x = \frac{-5}{4}x=4−5​.

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

Solve the equation $|4 x-1|=6$ for $x$ .

Assumptions1. The equation is $|4x -1| =6$ . We need to find the equivalent equations without the absolute value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|a| = b$ has two solutions $a = b$ and $a = -b$ . We can apply this concept to our equation.

Applying this concept to our equation, we get two equations1. $x -1 =6$
2. $x -1 = -6$

Now, we solve the first equation for $x$ .
$4x -1 =6$

Add1 to both sides of the equation to isolate $4x$ on one side.
$4x = +1$

Calculate the right side of the equation.
$4x =$

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{7}{4}$

Now, we solve the second equation for $x$ .
$4x -1 = -6$

Add to both sides of the equation to isolate $4x$ on one side.
$4x = -6 +$

Calculate the right side of the equation.
$4x = -5$

Divide both sides of the equation by4 to solve for $x$ .
$x = \frac{-5}{4}$ The equation $|4x -| =6$ is equivalent to $x = \frac{7}{4}$ or $x = \frac{-5}{4}$ .