QuestionSolve the equation $|6x + 7| = 49$ . List all solutions separated by commas.

Studdy Solution

STEP 1

Assumptions1. The equation is $|6x +7| =49$ . The absolute value of a number is its distance from zero on the number line, so it is always positive or zero.
3. The equation $|a| = b$ has two solutions $a = b$ and $a = -b$ if $b \geq0$ .

STEP 2

We can write the given equation as two separate equations without absolute values, based on the property of absolute values.
$6x +7 =49$ and $6x +7 = -49$

STEP 3

We will solve the first equation for $x$ . Start by subtracting7 from both sides.
$6x =49 -7$

STEP 4

Now, simplify the right side of the equation.
$6x =42$

STEP 5

Next, divide both sides by to solve for $x$ .
$x =42 /$

STEP 6

Calculate the value of $x$ .
$x =$

STEP 7

Now, we will solve the second equation for $x$ . Start by subtracting7 from both sides.
$6x = -49 -7$

STEP 8

Now, simplify the right side of the equation.
$6x = -56$

STEP 9

Next, divide both sides by6 to solve for $x$ .
$x = -56 /6$

STEP 10

Calculate the value of $x$ .
$x = -56 /6 = -\frac{28}{3}$ The solutions to the equation $|6x +7| =49$ are $x =7$ and $x = -\frac{28}{3}$ .

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QuestionSolve the equation $|6x + 7| = 49$ . List all solutions separated by commas.

Studdy Solution

STEP 1

Assumptions1. The equation is $|6x +7| =49$ . The absolute value of a number is its distance from zero on the number line, so it is always positive or zero.
3. The equation $|a| = b$ has two solutions $a = b$ and $a = -b$ if $b \geq0$ .

STEP 2

We can write the given equation as two separate equations without absolute values, based on the property of absolute values.
$6x +7 =49$ and $6x +7 = -49$

STEP 3

We will solve the first equation for $x$ . Start by subtracting7 from both sides.
$6x =49 -7$

STEP 4

Now, simplify the right side of the equation.
$6x =42$

STEP 5

Next, divide both sides by to solve for $x$ .
$x =42 /$

STEP 6

Calculate the value of $x$ .
$x =$

STEP 7

Now, we will solve the second equation for $x$ . Start by subtracting7 from both sides.
$6x = -49 -7$

STEP 8

Now, simplify the right side of the equation.
$6x = -56$

STEP 9

Next, divide both sides by6 to solve for $x$ .
$x = -56 /6$

STEP 10

Calculate the value of $x$ .
$x = -56 /6 = -\frac{28}{3}$ The solutions to the equation $|6x +7| =49$ are $x =7$ and $x = -\frac{28}{3}$ .

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QuestionSolve the equation ∣6x+7∣=49|6x + 7| = 49∣6x+7∣=49. List all solutions separated by commas.

Studdy Solution

STEP 1

Assumptions1. The equation is ∣6x+7∣=49|6x +7| =49∣6x+7∣=49 . The absolute value of a number is its distance from zero on the number line, so it is always positive or zero.3. The equation ∣a∣=b|a| = b∣a∣=b has two solutions a=ba = ba=b and a=−ba = -ba=−b if b≥0b \geq0b≥0.

STEP 2

We can write the given equation as two separate equations without absolute values, based on the property of absolute values.6x+7=496x +7 =496x+7=49and6x+7=−496x +7 = -496x+7=−49

STEP 3

We will solve the first equation for xxx. Start by subtracting7 from both sides.6x=49−76x =49 -76x=49−7

STEP 4

Now, simplify the right side of the equation.6x=426x =426x=42

STEP 5

Next, divide both sides by to solve for xxx.x=42/x =42 /x=42/

STEP 6

Calculate the value of xxx.x=x =x=

STEP 7

Now, we will solve the second equation for xxx. Start by subtracting7 from both sides.6x=−49−76x = -49 -76x=−49−7

STEP 8

Now, simplify the right side of the equation.6x=−566x = -566x=−56

STEP 9

Next, divide both sides by6 to solve for xxx.x=−56/6x = -56 /6x=−56/6

STEP 10

Calculate the value of xxx.x=−56/6=−283x = -56 /6 = -\frac{28}{3}x=−56/6=−328​The solutions to the equation ∣6x+7∣=49|6x +7| =49∣6x+7∣=49 are x=7x =7x=7 and x=−283x = -\frac{28}{3}x=−328​.

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QuestionSolve the equation $|6x + 7| = 49$ . List all solutions separated by commas.

Assumptions1. The equation is $|6x +7| =49$ . The absolute value of a number is its distance from zero on the number line, so it is always positive or zero.
3. The equation $|a| = b$ has two solutions $a = b$ and $a = -b$ if $b \geq0$ .

We can write the given equation as two separate equations without absolute values, based on the property of absolute values.
$6x +7 =49$ and $6x +7 = -49$

We will solve the first equation for $x$ . Start by subtracting7 from both sides.
$6x =49 -7$

Now, simplify the right side of the equation.
$6x =42$

Next, divide both sides by to solve for $x$ .
$x =42 /$

Calculate the value of $x$ .
$x =$

Now, we will solve the second equation for $x$ . Start by subtracting7 from both sides.
$6x = -49 -7$

Now, simplify the right side of the equation.
$6x = -56$

Next, divide both sides by6 to solve for $x$ .
$x = -56 /6$

Calculate the value of $x$ .
$x = -56 /6 = -\frac{28}{3}$ The solutions to the equation $|6x +7| =49$ are $x =7$ and $x = -\frac{28}{3}$ .