QuestionSolve the equation: $|2 - \frac{4x}{7}| = 6$ . Choose the correct answer set: A. or B. ( $\varnothing$ ).

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is the distance of the number from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is given by $\left|-\frac{4 x}{7}\right|=6$ .
3. We are asked to solve for $x$ .

STEP 2

An absolute value equation is actually two separate equations one where the expression inside the absolute value is equal to the positive value on the other side of the equation, and one where it is equal to the negative of that value. Therefore, we can write two equations from the given absolute value equation.
$2-\frac{4 x}{7}=6$ and $2-\frac{4 x}{7}=-6$

STEP 3

Let's solve the first equation $2-\frac{ x}{7}=6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{ x}{7}=6-2$

STEP 4

implify the right side of the equation.
$-\frac{4 x}{7}=4$

STEP 5

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x =4 \times -\frac{7}{4}$

STEP 6

implify the right side of the equation to find the value of $x$ .
$x = -$

STEP 7

Now, let's solve the second equation $2-\frac{4 x}{7}=-6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{4 x}{7}=-6-2$

STEP 8

implify the right side of the equation.
$-\frac{4 x}{7}=-8$

STEP 9

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x = -8 \times -\frac{7}{4}$

STEP 10

implify the right side of the equation to find the value of $x$ .
$x =14$

STEP 11

The solution set is $\{-7,14\}$ .
The solution is A. The solution set is $\{-7,14\}$ .

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QuestionSolve the equation: $|2 - \frac{4x}{7}| = 6$ . Choose the correct answer set: A. or B. ( $\varnothing$ ).

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is the distance of the number from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is given by $\left|-\frac{4 x}{7}\right|=6$ .
3. We are asked to solve for $x$ .

STEP 2

STEP 3

Let's solve the first equation $2-\frac{ x}{7}=6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{ x}{7}=6-2$

STEP 4

implify the right side of the equation.
$-\frac{4 x}{7}=4$

STEP 5

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x =4 \times -\frac{7}{4}$

STEP 6

implify the right side of the equation to find the value of $x$ .
$x = -$

STEP 7

Now, let's solve the second equation $2-\frac{4 x}{7}=-6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{4 x}{7}=-6-2$

STEP 8

implify the right side of the equation.
$-\frac{4 x}{7}=-8$

STEP 9

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x = -8 \times -\frac{7}{4}$

STEP 10

implify the right side of the equation to find the value of $x$ .
$x =14$

STEP 11

The solution set is $\{-7,14\}$ .
The solution is A. The solution set is $\{-7,14\}$ .

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QuestionSolve the equation: ∣2−4x7∣=6|2 - \frac{4x}{7}| = 6∣2−74x​∣=6. Choose the correct answer set: A. or B. (∅\varnothing∅).

Studdy Solution

STEP 1

STEP 2

STEP 3

Let's solve the first equation 2−x7=62-\frac{ x}{7}=62−7x​=6 for xxx.First, isolate the term with xxx on one side of the equation. We can do this by subtracting2 from both sides of the equation.−x7=6−2-\frac{ x}{7}=6-2−7x​=6−2

STEP 4

implify the right side of the equation.−4x7=4-\frac{4 x}{7}=4−74x​=4

STEP 5

To solve for xxx, multiply both sides of the equation by −74-\frac{7}{4}−47​.x=4×−74x =4 \times -\frac{7}{4}x=4×−47​

STEP 6

implify the right side of the equation to find the value of xxx.x=−x = -x=−

STEP 7

Now, let's solve the second equation 2−4x7=−62-\frac{4 x}{7}=-62−74x​=−6 for xxx.First, isolate the term with xxx on one side of the equation. We can do this by subtracting2 from both sides of the equation.−4x7=−6−2-\frac{4 x}{7}=-6-2−74x​=−6−2

STEP 8

implify the right side of the equation.−4x7=−8-\frac{4 x}{7}=-8−74x​=−8

STEP 9

To solve for xxx, multiply both sides of the equation by −74-\frac{7}{4}−47​.x=−8×−74x = -8 \times -\frac{7}{4}x=−8×−47​

STEP 10

implify the right side of the equation to find the value of xxx.x=14x =14x=14

STEP 11

The solution set is {−7,14}\{-7,14\}{−7,14}.The solution is A. The solution set is {−7,14}\{-7,14\}{−7,14}.

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QuestionSolve the equation: $|2 - \frac{4x}{7}| = 6$ . Choose the correct answer set: A. or B. ( $\varnothing$ ).

Let's solve the first equation $2-\frac{ x}{7}=6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{ x}{7}=6-2$

implify the right side of the equation.
$-\frac{4 x}{7}=4$

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x =4 \times -\frac{7}{4}$

implify the right side of the equation to find the value of $x$ .
$x = -$

Now, let's solve the second equation $2-\frac{4 x}{7}=-6$ for $x$ .
First, isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$-\frac{4 x}{7}=-6-2$

implify the right side of the equation.
$-\frac{4 x}{7}=-8$

To solve for $x$ , multiply both sides of the equation by $-\frac{7}{4}$ .
$x = -8 \times -\frac{7}{4}$

implify the right side of the equation to find the value of $x$ .
$x =14$

The solution set is $\{-7,14\}$ .
The solution is A. The solution set is $\{-7,14\}$ .