QuestionFind the solution set for the equation: $-3|1-x|-2=-14$ . Options: $\{-5,3\}$ , $\{-3,5\}$ , $\{3,-5\}$ , $\{5,3\}$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-3|1-x|-=-14$ . We are looking for the solution set, which means we are looking for the values of $x$ that satisfy the equation.

STEP 2

First, we need to isolate the absolute value term. We can do this by adding2 to both sides of the equation.
$-|1-x| = -14 +2$

STEP 3

Now, simplify the right side of the equation.
$-3|1-x| = -12$

STEP 4

Next, we need to get rid of the coefficient of the absolute value term. We can do this by dividing both sides of the equation by -3.
$|1-x| = -12 / -3$

STEP 5

implify the right side of the equation.
$|1-x| =4$

STEP 6

The absolute value of a number is always non-negative. Therefore, the equation $|1-x|=4$ breaks down into two possible equations $1-x=4$ and $1-x=-4$ .

STEP 7

olve the first equation for $x$ .
$1-x=4$ $x=1-4$

STEP 8

Calculate the value of $x$ .
$x=1-4=-3$

STEP 9

Now, solve the second equation for $x$ .
$-x=-4$ $x=-(-4)$

STEP 10

Calculate the value of $x$ .
$x=-(-4)=5$ The solution set for the equation is $\{-3,5\}$ .

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QuestionFind the solution set for the equation: $-3|1-x|-2=-14$ . Options: $\{-5,3\}$ , $\{-3,5\}$ , $\{3,-5\}$ , $\{5,3\}$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-3|1-x|-=-14$ . We are looking for the solution set, which means we are looking for the values of $x$ that satisfy the equation.

STEP 2

First, we need to isolate the absolute value term. We can do this by adding2 to both sides of the equation.
$-|1-x| = -14 +2$

STEP 3

Now, simplify the right side of the equation.
$-3|1-x| = -12$

STEP 4

Next, we need to get rid of the coefficient of the absolute value term. We can do this by dividing both sides of the equation by -3.
$|1-x| = -12 / -3$

STEP 5

implify the right side of the equation.
$|1-x| =4$

STEP 6

The absolute value of a number is always non-negative. Therefore, the equation $|1-x|=4$ breaks down into two possible equations $1-x=4$ and $1-x=-4$ .

STEP 7

olve the first equation for $x$ .
$1-x=4$ $x=1-4$

STEP 8

Calculate the value of $x$ .
$x=1-4=-3$

STEP 9

Now, solve the second equation for $x$ .
$-x=-4$ $x=-(-4)$

STEP 10

Calculate the value of $x$ .
$x=-(-4)=5$ The solution set for the equation is $\{-3,5\}$ .

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QuestionFind the solution set for the equation: −3∣1−x∣−2=−14-3|1-x|-2=-14−3∣1−x∣−2=−14. Options: {−5,3}\{-5,3\}{−5,3}, {−3,5}\{-3,5\}{−3,5}, {3,−5}\{3,-5\}{3,−5}, {5,3}\{5,3\}{5,3}.

Studdy Solution

STEP 1

Assumptions1. The given equation is −3∣1−x∣−=−14-3|1-x|-=-14−3∣1−x∣−=−14 . We are looking for the solution set, which means we are looking for the values of xxx that satisfy the equation.

STEP 2

First, we need to isolate the absolute value term. We can do this by adding2 to both sides of the equation.−∣1−x∣=−14+2-|1-x| = -14 +2−∣1−x∣=−14+2

STEP 3

Now, simplify the right side of the equation.−3∣1−x∣=−12-3|1-x| = -12−3∣1−x∣=−12

STEP 4

Next, we need to get rid of the coefficient of the absolute value term. We can do this by dividing both sides of the equation by -3.∣1−x∣=−12/−3|1-x| = -12 / -3∣1−x∣=−12/−3

STEP 5

implify the right side of the equation.∣1−x∣=4|1-x| =4∣1−x∣=4

STEP 6

The absolute value of a number is always non-negative. Therefore, the equation ∣1−x∣=4|1-x|=4∣1−x∣=4 breaks down into two possible equations 1−x=41-x=41−x=4 and 1−x=−41-x=-41−x=−4.

STEP 7

olve the first equation for xxx.1−x=41-x=41−x=4x=1−4x=1-4x=1−4

STEP 8

Calculate the value of xxx.x=1−4=−3x=1-4=-3x=1−4=−3

STEP 9

Now, solve the second equation for xxx.−x=−4-x=-4−x=−4x=−(−4)x=-(-4)x=−(−4)

STEP 10

Calculate the value of xxx.x=−(−4)=5x=-(-4)=5x=−(−4)=5The solution set for the equation is {−3,5}\{-3,5\}{−3,5}.

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QuestionFind the solution set for the equation: $-3|1-x|-2=-14$ . Options: $\{-5,3\}$ , $\{-3,5\}$ , $\{3,-5\}$ , $\{5,3\}$ .

Assumptions1. The given equation is $-3|1-x|-=-14$ . We are looking for the solution set, which means we are looking for the values of $x$ that satisfy the equation.

First, we need to isolate the absolute value term. We can do this by adding2 to both sides of the equation.
$-|1-x| = -14 +2$

Now, simplify the right side of the equation.
$-3|1-x| = -12$

Next, we need to get rid of the coefficient of the absolute value term. We can do this by dividing both sides of the equation by -3.
$|1-x| = -12 / -3$

implify the right side of the equation.
$|1-x| =4$

The absolute value of a number is always non-negative. Therefore, the equation $|1-x|=4$ breaks down into two possible equations $1-x=4$ and $1-x=-4$ .

olve the first equation for $x$ .
$1-x=4$ $x=1-4$

Calculate the value of $x$ .
$x=1-4=-3$

Now, solve the second equation for $x$ .
$-x=-4$ $x=-(-4)$

Calculate the value of $x$ .
$x=-(-4)=5$ The solution set for the equation is $\{-3,5\}$ .