Solved on Sep 25, 2023

Solve the equation $|3x-4|=18$ to find the possible values of $x$ .

STEP 1

Assumptions1. The equation is $|3x -4| =18$ . We are looking for the solutions for $x$ that satisfy this equation

STEP 2

The absolute value function $|x|$ is defined as $|x| =\begin{cases}x & \text{if } x \geq0 \\ -x & \text{if } x <0\end{cases}$ So, the equation $|x -4| =18$ can be split into two cases1. $x -4 =18$ when $x -4 \geq0$
2. $x -4 = -18$ when $x -4 <0$

STEP 3

Let's solve the first case $3x - =18$
Add to both sides of the equation to isolate $3x$ on one side.
$3x =18 +$

STEP 4

Calculate the right side of the equation.
$3x =22$

STEP 5

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{22}{3}$

STEP 6

Now, let's solve the second case $3x -4 = -18$
Add4 to both sides of the equation to isolate $3x$ on one side.
$3x = -18 +4$

STEP 7

Calculate the right side of the equation.
$3x = -14$

STEP 8

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{-14}{3}$ So, the solutions to the equation $|3x -4| =18$ are $x = \frac{22}{3}$ and $x = \frac{-14}{3}$ .

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Solve the equation $|3x-4|=18$ to find the possible values of $x$ .

STEP 1

Assumptions1. The equation is $|3x -4| =18$ . We are looking for the solutions for $x$ that satisfy this equation

STEP 2

The absolute value function $|x|$ is defined as $|x| =\begin{cases}x & \text{if } x \geq0 \\ -x & \text{if } x <0\end{cases}$ So, the equation $|x -4| =18$ can be split into two cases1. $x -4 =18$ when $x -4 \geq0$
2. $x -4 = -18$ when $x -4 <0$

STEP 3

Let's solve the first case $3x - =18$
Add to both sides of the equation to isolate $3x$ on one side.
$3x =18 +$

STEP 4

Calculate the right side of the equation.
$3x =22$

STEP 5

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{22}{3}$

STEP 6

Now, let's solve the second case $3x -4 = -18$
Add4 to both sides of the equation to isolate $3x$ on one side.
$3x = -18 +4$

STEP 7

Calculate the right side of the equation.
$3x = -14$

STEP 8

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{-14}{3}$ So, the solutions to the equation $|3x -4| =18$ are $x = \frac{22}{3}$ and $x = \frac{-14}{3}$ .

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Solve the equation ∣3x−4∣=18|3x-4|=18∣3x−4∣=18 to find the possible values of xxx.

STEP 1

Assumptions1. The equation is ∣3x−4∣=18|3x -4| =18∣3x−4∣=18 . We are looking for the solutions for xxx that satisfy this equation

STEP 2

STEP 3

Let's solve the first case 3x−=183x - =183x−=18Add to both sides of the equation to isolate 3x3x3x on one side.3x=18+3x =18 +3x=18+

STEP 4

Calculate the right side of the equation.3x=223x =223x=22

STEP 5

Divide both sides of the equation by3 to solve for xxx.x=223x = \frac{22}{3}x=322​

STEP 6

Now, let's solve the second case 3x−4=−183x -4 = -183x−4=−18Add4 to both sides of the equation to isolate 3x3x3x on one side.3x=−18+43x = -18 +43x=−18+4

STEP 7

Calculate the right side of the equation.3x=−143x = -143x=−14

STEP 8

Divide both sides of the equation by3 to solve for xxx.x=−143x = \frac{-14}{3}x=3−14​So, the solutions to the equation ∣3x−4∣=18|3x -4| =18∣3x−4∣=18 are x=223x = \frac{22}{3}x=322​ and x=−143x = \frac{-14}{3}x=3−14​.

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Solve the equation $|3x-4|=18$ to find the possible values of $x$ .

Assumptions1. The equation is $|3x -4| =18$ . We are looking for the solutions for $x$ that satisfy this equation

Let's solve the first case $3x - =18$
Add to both sides of the equation to isolate $3x$ on one side.
$3x =18 +$

Calculate the right side of the equation.
$3x =22$

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{22}{3}$

Now, let's solve the second case $3x -4 = -18$
Add4 to both sides of the equation to isolate $3x$ on one side.
$3x = -18 +4$

Calculate the right side of the equation.
$3x = -14$

Divide both sides of the equation by3 to solve for $x$ .
$x = \frac{-14}{3}$ So, the solutions to the equation $|3x -4| =18$ are $x = \frac{22}{3}$ and $x = \frac{-14}{3}$ .