Solved on Jan 20, 2024

Find $x$ that satisfies $5x - 3 = 12x + 11$ . The solution set is...

STEP 1

Assumptions
1. We are given the linear equation $5x - 3 = 12x + 11$ .
2. We need to find the value of $x$ that satisfies the equation.

STEP 2

First, we want to collect like terms on one side of the equation to isolate the variable $x$ . We can do this by subtracting $5x$ from both sides of the equation.
$5x - 3 - 5x = 12x + 11 - 5x$

STEP 3

Simplify both sides of the equation by combining like terms.
$-3 = 7x + 11$

STEP 4

Next, we want to isolate the term containing $x$ by subtracting 11 from both sides of the equation.
$-3 - 11 = 7x + 11 - 11$

STEP 5

Simplify both sides of the equation by combining like terms.
$-14 = 7x$

STEP 6

Now, we want to solve for $x$ by dividing both sides of the equation by 7.
$\frac{-14}{7} = \frac{7x}{7}$

STEP 7

Simplify both sides of the equation to find the value of $x$ .
$x = -2$
The solution set is $\{x \mid x = -2\}$ .

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Find $x$ that satisfies $5x - 3 = 12x + 11$ . The solution set is...

STEP 1

Assumptions
1. We are given the linear equation $5x - 3 = 12x + 11$ .
2. We need to find the value of $x$ that satisfies the equation.

STEP 2

First, we want to collect like terms on one side of the equation to isolate the variable $x$ . We can do this by subtracting $5x$ from both sides of the equation.
$5x - 3 - 5x = 12x + 11 - 5x$

STEP 3

Simplify both sides of the equation by combining like terms.
$-3 = 7x + 11$

STEP 4

Next, we want to isolate the term containing $x$ by subtracting 11 from both sides of the equation.
$-3 - 11 = 7x + 11 - 11$

STEP 5

Simplify both sides of the equation by combining like terms.
$-14 = 7x$

STEP 6

Now, we want to solve for $x$ by dividing both sides of the equation by 7.
$\frac{-14}{7} = \frac{7x}{7}$

STEP 7

Simplify both sides of the equation to find the value of $x$ .
$x = -2$
The solution set is $\{x \mid x = -2\}$ .

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Find xxx that satisfies 5x−3=12x+115x - 3 = 12x + 115x−3=12x+11. The solution set is...

STEP 1

Assumptions1. We are given the linear equation 5x−3=12x+115x - 3 = 12x + 115x−3=12x+11.2. We need to find the value of xxx that satisfies the equation.

STEP 2

First, we want to collect like terms on one side of the equation to isolate the variable xxx. We can do this by subtracting 5x5x5x from both sides of the equation.5x−3−5x=12x+11−5x5x - 3 - 5x = 12x + 11 - 5x5x−3−5x=12x+11−5x

STEP 3

Simplify both sides of the equation by combining like terms.−3=7x+11-3 = 7x + 11−3=7x+11

STEP 4

Next, we want to isolate the term containing xxx by subtracting 11 from both sides of the equation.−3−11=7x+11−11-3 - 11 = 7x + 11 - 11−3−11=7x+11−11

STEP 5

Simplify both sides of the equation by combining like terms.−14=7x-14 = 7x−14=7x

STEP 6

Now, we want to solve for xxx by dividing both sides of the equation by 7.−147=7x7\frac{-14}{7} = \frac{7x}{7}7−14​=77x​

STEP 7

Simplify both sides of the equation to find the value of xxx.x=−2x = -2x=−2The solution set is {x∣x=−2}\{x \mid x = -2\}{x∣x=−2}.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find $x$ that satisfies $5x - 3 = 12x + 11$ . The solution set is...

Assumptions
1. We are given the linear equation $5x - 3 = 12x + 11$ .
2. We need to find the value of $x$ that satisfies the equation.

First, we want to collect like terms on one side of the equation to isolate the variable $x$ . We can do this by subtracting $5x$ from both sides of the equation.
$5x - 3 - 5x = 12x + 11 - 5x$

Simplify both sides of the equation by combining like terms.
$-3 = 7x + 11$

Next, we want to isolate the term containing $x$ by subtracting 11 from both sides of the equation.
$-3 - 11 = 7x + 11 - 11$

Simplify both sides of the equation by combining like terms.
$-14 = 7x$

Now, we want to solve for $x$ by dividing both sides of the equation by 7.
$\frac{-14}{7} = \frac{7x}{7}$

Simplify both sides of the equation to find the value of $x$ .
$x = -2$
The solution set is $\{x \mid x = -2\}$ .