Solved on Jan 12, 2024

Solve for $u$ in the equation $-6 u-28=-2(u-6)$ . Simplify the solution.

STEP 1

Assumptions
1. We are given the equation $-6u - 28 = -2(u - 6)$ .
2. We need to solve for the variable $u$ .
3. The equation is linear.

STEP 2

First, we will distribute the $-2$ on the right side of the equation to both terms inside the parentheses.
$-6u - 28 = -2(u - 6)$

STEP 3

Apply the distribution.
$-6u - 28 = -2u + 12$

STEP 4

Next, we will move all terms containing $u$ to one side of the equation and the constant terms to the other side. To do this, we will add $2u$ to both sides of the equation.
$-6u + 2u - 28 = -2u + 2u + 12$

STEP 5

Simplify both sides of the equation.
$-4u - 28 = 12$

STEP 6

Now, we will add $28$ to both sides of the equation to isolate the term with $u$ on one side.
$-4u - 28 + 28 = 12 + 28$

STEP 7

Simplify both sides of the equation.
$-4u = 40$

STEP 8

To solve for $u$ , we will divide both sides of the equation by $-4$ .
$\frac{-4u}{-4} = \frac{40}{-4}$

STEP 9

Simplify both sides of the equation to find the value of $u$ .
$u = -10$
The solution for $u$ is $-10$ .

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Solve for $u$ in the equation $-6 u-28=-2(u-6)$ . Simplify the solution.

STEP 1

Assumptions
1. We are given the equation $-6u - 28 = -2(u - 6)$ .
2. We need to solve for the variable $u$ .
3. The equation is linear.

STEP 2

First, we will distribute the $-2$ on the right side of the equation to both terms inside the parentheses.
$-6u - 28 = -2(u - 6)$

STEP 3

Apply the distribution.
$-6u - 28 = -2u + 12$

STEP 4

Next, we will move all terms containing $u$ to one side of the equation and the constant terms to the other side. To do this, we will add $2u$ to both sides of the equation.
$-6u + 2u - 28 = -2u + 2u + 12$

STEP 5

Simplify both sides of the equation.
$-4u - 28 = 12$

STEP 6

Now, we will add $28$ to both sides of the equation to isolate the term with $u$ on one side.
$-4u - 28 + 28 = 12 + 28$

STEP 7

Simplify both sides of the equation.
$-4u = 40$

STEP 8

To solve for $u$ , we will divide both sides of the equation by $-4$ .
$\frac{-4u}{-4} = \frac{40}{-4}$

STEP 9

Simplify both sides of the equation to find the value of $u$ .
$u = -10$
The solution for $u$ is $-10$ .

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Solve for uuu in the equation −6u−28=−2(u−6)-6 u-28=-2(u-6)−6u−28=−2(u−6). Simplify the solution.

STEP 1

Assumptions1. We are given the equation −6u−28=−2(u−6)-6u - 28 = -2(u - 6)−6u−28=−2(u−6).2. We need to solve for the variable uuu.3. The equation is linear.

STEP 2

First, we will distribute the −2-2−2 on the right side of the equation to both terms inside the parentheses.−6u−28=−2(u−6)-6u - 28 = -2(u - 6)−6u−28=−2(u−6)

STEP 3

Apply the distribution.−6u−28=−2u+12-6u - 28 = -2u + 12−6u−28=−2u+12

STEP 4

Next, we will move all terms containing uuu to one side of the equation and the constant terms to the other side. To do this, we will add 2u2u2u to both sides of the equation.−6u+2u−28=−2u+2u+12-6u + 2u - 28 = -2u + 2u + 12−6u+2u−28=−2u+2u+12

STEP 5

Simplify both sides of the equation.−4u−28=12-4u - 28 = 12−4u−28=12

STEP 6

Now, we will add 282828 to both sides of the equation to isolate the term with uuu on one side.−4u−28+28=12+28-4u - 28 + 28 = 12 + 28−4u−28+28=12+28

STEP 7

Simplify both sides of the equation.−4u=40-4u = 40−4u=40

STEP 8

To solve for uuu, we will divide both sides of the equation by −4-4−4.−4u−4=40−4\frac{-4u}{-4} = \frac{40}{-4}−4−4u​=−440​

STEP 9

Simplify both sides of the equation to find the value of uuu.u=−10u = -10u=−10The solution for uuu is −10-10−10.

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Solve for $u$ in the equation $-6 u-28=-2(u-6)$ . Simplify the solution.

Assumptions
1. We are given the equation $-6u - 28 = -2(u - 6)$ .
2. We need to solve for the variable $u$ .
3. The equation is linear.

First, we will distribute the $-2$ on the right side of the equation to both terms inside the parentheses.
$-6u - 28 = -2(u - 6)$

Apply the distribution.
$-6u - 28 = -2u + 12$

Next, we will move all terms containing $u$ to one side of the equation and the constant terms to the other side. To do this, we will add $2u$ to both sides of the equation.
$-6u + 2u - 28 = -2u + 2u + 12$

Simplify both sides of the equation.
$-4u - 28 = 12$

Now, we will add $28$ to both sides of the equation to isolate the term with $u$ on one side.
$-4u - 28 + 28 = 12 + 28$

Simplify both sides of the equation.
$-4u = 40$

To solve for $u$ , we will divide both sides of the equation by $-4$ .
$\frac{-4u}{-4} = \frac{40}{-4}$

Simplify both sides of the equation to find the value of $u$ .
$u = -10$
The solution for $u$ is $-10$ .