QuestionSolve the equation: $|x-3|=17$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $|x-3|=17$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.

STEP 2

The absolute value equation $|x-|=17$ can be rewritten as two separate equations. This is because the distance from $x$ to $$ on the number line can be $17$ units to the right or $17$ units to the left.
$x- =17 \quad or \quad x- = -17$

STEP 3

Now, we solve each equation separately. First, we solve $x-3 =17$ .
$x =17 +3$

STEP 4

Calculate the value of $x$ .
$x =17 +3 =20$

STEP 5

Next, we solve the second equation $x-3 = -17$ .
$x = -17 +3$

STEP 6

Calculate the value of $x$ .
$x = -17 +3 = -14$ So, the solutions to the equation $|x-3|=17$ are $x=20$ and $x=-14$ .

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QuestionSolve the equation: $|x-3|=17$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $|x-3|=17$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.

STEP 2

The absolute value equation $|x-|=17$ can be rewritten as two separate equations. This is because the distance from $x$ to $$ on the number line can be $17$ units to the right or $17$ units to the left.
$x- =17 \quad or \quad x- = -17$

STEP 3

Now, we solve each equation separately. First, we solve $x-3 =17$ .
$x =17 +3$

STEP 4

Calculate the value of $x$ .
$x =17 +3 =20$

STEP 5

Next, we solve the second equation $x-3 = -17$ .
$x = -17 +3$

STEP 6

Calculate the value of $x$ .
$x = -17 +3 = -14$ So, the solutions to the equation $|x-3|=17$ are $x=20$ and $x=-14$ .

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QuestionSolve the equation: ∣x−3∣=17|x-3|=17∣x−3∣=17.

Studdy Solution

STEP 1

Assumptions1. The given equation is ∣x−3∣=17|x-3|=17∣x−3∣=17 . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.

STEP 2

The absolute value equation ∣x−∣=17|x-|=17∣x−∣=17 can be rewritten as two separate equations. This is because the distance from xxx to $$ on the number line can be $17$ units to the right or $17$ units to the left.x−=17orx−=−17x- =17 \quad or \quad x- = -17x−=17orx−=−17

STEP 3

Now, we solve each equation separately. First, we solve x−3=17x-3 =17x−3=17.x=17+3x =17 +3x=17+3

STEP 4

Calculate the value of xxx.x=17+3=20x =17 +3 =20x=17+3=20

STEP 5

Next, we solve the second equation x−3=−17x-3 = -17x−3=−17.x=−17+3x = -17 +3x=−17+3

STEP 6

Calculate the value of xxx.x=−17+3=−14x = -17 +3 = -14x=−17+3=−14So, the solutions to the equation ∣x−3∣=17|x-3|=17∣x−3∣=17 are x=20x=20x=20 and x=−14x=-14x=−14.

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QuestionSolve the equation: $|x-3|=17$ .

Assumptions1. The given equation is $|x-3|=17$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.

The absolute value equation $|x-|=17$ can be rewritten as two separate equations. This is because the distance from $x$ to $$ on the number line can be $17$ units to the right or $17$ units to the left.
$x- =17 \quad or \quad x- = -17$

Now, we solve each equation separately. First, we solve $x-3 =17$ .
$x =17 +3$

Calculate the value of $x$ .
$x =17 +3 =20$

Next, we solve the second equation $x-3 = -17$ .
$x = -17 +3$

Calculate the value of $x$ .
$x = -17 +3 = -14$ So, the solutions to the equation $|x-3|=17$ are $x=20$ and $x=-14$ .