Solved on Jan 20, 2024

Solve for $x$ in the linear equation $8x + 3 = 6x - 9$ , then evaluate $3x - 2$ .

STEP 1

Assumptions
1. We have the equation $8x + 3 = 6x - 9$ .
2. We need to find the value of $3x - 2$ .

STEP 2

First, we need to solve the given equation for $x$ . We can start by moving all terms containing $x$ to one side of the equation.
$8x - 6x + 3 = 6x - 6x - 9$

STEP 3

Simplify both sides of the equation by combining like terms.
$2x + 3 = -9$

STEP 4

Next, we will isolate $x$ by moving the constant term on the left side of the equation to the right side.
$2x = -9 - 3$

STEP 5

Simplify the right side of the equation by combining the constants.
$2x = -12$

STEP 6

Now, divide both sides of the equation by the coefficient of $x$ to solve for $x$ .
$x = \frac{-12}{2}$

STEP 7

Calculate the value of $x$ .
$x = -6$

STEP 8

Now that we have the value of $x$ , we can evaluate $3x - 2$ by substituting $x$ with its value.
$3x - 2 = 3(-6) - 2$

STEP 9

Multiply $3$ by $-6$ .
$3x - 2 = -18 - 2$

STEP 10

Combine the constants to find the value of $3x - 2$ .
$3x - 2 = -20$
The value of $3x - 2$ is $-20$ .

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Solve for $x$ in the linear equation $8x + 3 = 6x - 9$ , then evaluate $3x - 2$ .

STEP 1

Assumptions
1. We have the equation $8x + 3 = 6x - 9$ .
2. We need to find the value of $3x - 2$ .

STEP 2

First, we need to solve the given equation for $x$ . We can start by moving all terms containing $x$ to one side of the equation.
$8x - 6x + 3 = 6x - 6x - 9$

STEP 3

Simplify both sides of the equation by combining like terms.
$2x + 3 = -9$

STEP 4

Next, we will isolate $x$ by moving the constant term on the left side of the equation to the right side.
$2x = -9 - 3$

STEP 5

Simplify the right side of the equation by combining the constants.
$2x = -12$

STEP 6

Now, divide both sides of the equation by the coefficient of $x$ to solve for $x$ .
$x = \frac{-12}{2}$

STEP 7

Calculate the value of $x$ .
$x = -6$

STEP 8

Now that we have the value of $x$ , we can evaluate $3x - 2$ by substituting $x$ with its value.
$3x - 2 = 3(-6) - 2$

STEP 9

Multiply $3$ by $-6$ .
$3x - 2 = -18 - 2$

STEP 10

Combine the constants to find the value of $3x - 2$ .
$3x - 2 = -20$
The value of $3x - 2$ is $-20$ .

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Solve for xxx in the linear equation 8x+3=6x−98x + 3 = 6x - 98x+3=6x−9, then evaluate 3x−23x - 23x−2.

STEP 1

Assumptions1. We have the equation 8x+3=6x−98x + 3 = 6x - 98x+3=6x−9.2. We need to find the value of 3x−23x - 23x−2.

STEP 2

First, we need to solve the given equation for xxx. We can start by moving all terms containing xxx to one side of the equation.8x−6x+3=6x−6x−98x - 6x + 3 = 6x - 6x - 98x−6x+3=6x−6x−9

STEP 3

Simplify both sides of the equation by combining like terms.2x+3=−92x + 3 = -92x+3=−9

STEP 4

Next, we will isolate xxx by moving the constant term on the left side of the equation to the right side.2x=−9−32x = -9 - 32x=−9−3

STEP 5

Simplify the right side of the equation by combining the constants.2x=−122x = -122x=−12

STEP 6

Now, divide both sides of the equation by the coefficient of xxx to solve for xxx.x=−122x = \frac{-12}{2}x=2−12​

STEP 7

Calculate the value of xxx.x=−6x = -6x=−6

STEP 8

Now that we have the value of xxx, we can evaluate 3x−23x - 23x−2 by substituting xxx with its value.3x−2=3(−6)−23x - 2 = 3(-6) - 23x−2=3(−6)−2

STEP 9

Multiply 333 by −6-6−6.3x−2=−18−23x - 2 = -18 - 23x−2=−18−2

STEP 10

Combine the constants to find the value of 3x−23x - 23x−2.3x−2=−203x - 2 = -203x−2=−20The value of 3x−23x - 23x−2 is −20-20−20.

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Solve for $x$ in the linear equation $8x + 3 = 6x - 9$ , then evaluate $3x - 2$ .

Assumptions
1. We have the equation $8x + 3 = 6x - 9$ .
2. We need to find the value of $3x - 2$ .

First, we need to solve the given equation for $x$ . We can start by moving all terms containing $x$ to one side of the equation.
$8x - 6x + 3 = 6x - 6x - 9$

Simplify both sides of the equation by combining like terms.
$2x + 3 = -9$

Next, we will isolate $x$ by moving the constant term on the left side of the equation to the right side.
$2x = -9 - 3$

Simplify the right side of the equation by combining the constants.
$2x = -12$

Now, divide both sides of the equation by the coefficient of $x$ to solve for $x$ .
$x = \frac{-12}{2}$

Calculate the value of $x$ .
$x = -6$

Now that we have the value of $x$ , we can evaluate $3x - 2$ by substituting $x$ with its value.
$3x - 2 = 3(-6) - 2$

Multiply $3$ by $-6$ .
$3x - 2 = -18 - 2$

Combine the constants to find the value of $3x - 2$ .
$3x - 2 = -20$
The value of $3x - 2$ is $-20$ .