Question Simplify the inequality $x-2+6 x \neq 6+8 x$ and solve for $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality $x - 2 + 6x \neq 6 + 8x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will simplify both sides of the inequality by combining like terms.
On the left side, combine the terms with $x$ and the constant terms separately.
$x + 6x - 2 \neq 6 + 8x$

STEP 3

Simplify the left side by adding the coefficients of $x$ .
$7x - 2 \neq 6 + 8x$

STEP 4

Now, we will isolate the variable $x$ on one side of the inequality. To do this, we will move the term with $x$ from the right side to the left side by subtracting $8x$ from both sides.
$7x - 2 - 8x \neq 6 + 8x - 8x$

STEP 5

Simplify both sides of the inequality after subtracting $8x$ .
$-x - 2 \neq 6$

STEP 6

Next, we will move the constant term from the left side to the right side by adding $2$ to both sides.
$-x - 2 + 2 \neq 6 + 2$

STEP 7

Simplify both sides of the inequality after adding $2$ .
$-x \neq 8$

STEP 8

To solve for $x$ , we need to get rid of the negative sign in front of $x$ . We can do this by multiplying both sides of the inequality by $-1$ . Remember that when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality changes. However, since this is a "not equal to" inequality, the direction does not change.
$-1 \cdot (-x) \neq -1 \cdot 8$

STEP 9

Simplify both sides of the inequality after multiplying by $-1$ .
$x \neq -8$
The solution to the inequality is that $x$ cannot be equal to $-8$ .

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Question Simplify the inequality $x-2+6 x \neq 6+8 x$ and solve for $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality $x - 2 + 6x \neq 6 + 8x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will simplify both sides of the inequality by combining like terms.
On the left side, combine the terms with $x$ and the constant terms separately.
$x + 6x - 2 \neq 6 + 8x$

STEP 3

Simplify the left side by adding the coefficients of $x$ .
$7x - 2 \neq 6 + 8x$

STEP 4

Now, we will isolate the variable $x$ on one side of the inequality. To do this, we will move the term with $x$ from the right side to the left side by subtracting $8x$ from both sides.
$7x - 2 - 8x \neq 6 + 8x - 8x$

STEP 5

Simplify both sides of the inequality after subtracting $8x$ .
$-x - 2 \neq 6$

STEP 6

Next, we will move the constant term from the left side to the right side by adding $2$ to both sides.
$-x - 2 + 2 \neq 6 + 2$

STEP 7

Simplify both sides of the inequality after adding $2$ .
$-x \neq 8$

STEP 8

STEP 9

Simplify both sides of the inequality after multiplying by $-1$ .
$x \neq -8$
The solution to the inequality is that $x$ cannot be equal to $-8$ .

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Question Simplify the inequality x−2+6x≠6+8xx-2+6 x \neq 6+8 xx−2+6x=6+8x and solve for xxx.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality x−2+6x≠6+8xx - 2 + 6x \neq 6 + 8xx−2+6x=6+8x.2. We need to solve for the variable xxx.

STEP 2

First, we will simplify both sides of the inequality by combining like terms.On the left side, combine the terms with xxx and the constant terms separately.x+6x−2≠6+8xx + 6x - 2 \neq 6 + 8xx+6x−2=6+8x

STEP 3

Simplify the left side by adding the coefficients of xxx.7x−2≠6+8x7x - 2 \neq 6 + 8x7x−2=6+8x

STEP 4

Now, we will isolate the variable xxx on one side of the inequality. To do this, we will move the term with xxx from the right side to the left side by subtracting 8x8x8x from both sides.7x−2−8x≠6+8x−8x7x - 2 - 8x \neq 6 + 8x - 8x7x−2−8x=6+8x−8x

STEP 5

Simplify both sides of the inequality after subtracting 8x8x8x.−x−2≠6-x - 2 \neq 6−x−2=6

STEP 6

Next, we will move the constant term from the left side to the right side by adding 222 to both sides.−x−2+2≠6+2-x - 2 + 2 \neq 6 + 2−x−2+2=6+2

STEP 7

Simplify both sides of the inequality after adding 222.−x≠8-x \neq 8−x=8

STEP 8

STEP 9

Simplify both sides of the inequality after multiplying by −1-1−1.x≠−8x \neq -8x=−8The solution to the inequality is that xxx cannot be equal to −8-8−8.

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Question Simplify the inequality $x-2+6 x \neq 6+8 x$ and solve for $x$ .

Assumptions
1. We are given the inequality $x - 2 + 6x \neq 6 + 8x$ .
2. We need to solve for the variable $x$ .

First, we will simplify both sides of the inequality by combining like terms.
On the left side, combine the terms with $x$ and the constant terms separately.
$x + 6x - 2 \neq 6 + 8x$

Simplify the left side by adding the coefficients of $x$ .
$7x - 2 \neq 6 + 8x$

Now, we will isolate the variable $x$ on one side of the inequality. To do this, we will move the term with $x$ from the right side to the left side by subtracting $8x$ from both sides.
$7x - 2 - 8x \neq 6 + 8x - 8x$

Simplify both sides of the inequality after subtracting $8x$ .
$-x - 2 \neq 6$

Next, we will move the constant term from the left side to the right side by adding $2$ to both sides.
$-x - 2 + 2 \neq 6 + 2$

Simplify both sides of the inequality after adding $2$ .
$-x \neq 8$

Simplify both sides of the inequality after multiplying by $-1$ .
$x \neq -8$
The solution to the inequality is that $x$ cannot be equal to $-8$ .