Solved on Jan 23, 2024

Solve the equation $-6u-13=3-8u$ . The solution set is $\{u\}$ .

STEP 1

Assumptions
1. We are given the linear equation $-6u - 13 = 3 - 8u$ .
2. We need to solve for the variable $u$ .
3. The solution set will be in the form $\{u\}$ where $u$ is the value that satisfies the equation.

STEP 2

To solve for $u$ , we need to isolate the variable on one side of the equation. First, we can move all terms involving $u$ to one side of the equation by adding $8u$ to both sides.
$-6u - 13 + 8u = 3 - 8u + 8u$

STEP 3

Combine like terms on both sides of the equation.
$2u - 13 = 3$

STEP 4

Next, we can move the constant term from the left side to the right side by adding $13$ to both sides of the equation.
$2u - 13 + 13 = 3 + 13$

STEP 5

Combine the constant terms on the right side of the equation.
$2u = 16$

STEP 6

Now, we need to isolate $u$ by dividing both sides of the equation by the coefficient of $u$ , which is $2$ .
$\frac{2u}{2} = \frac{16}{2}$

STEP 7

Simplify both sides of the equation to find the value of $u$ .
$u = 8$

STEP 8

The solution set for the equation is the set containing the value of $u$ that satisfies the equation.
$\text{The solution set is } \{8\}.$

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Solve the equation $-6u-13=3-8u$ . The solution set is $\{u\}$ .

STEP 1

Assumptions
1. We are given the linear equation $-6u - 13 = 3 - 8u$ .
2. We need to solve for the variable $u$ .
3. The solution set will be in the form $\{u\}$ where $u$ is the value that satisfies the equation.

STEP 2

To solve for $u$ , we need to isolate the variable on one side of the equation. First, we can move all terms involving $u$ to one side of the equation by adding $8u$ to both sides.
$-6u - 13 + 8u = 3 - 8u + 8u$

STEP 3

Combine like terms on both sides of the equation.
$2u - 13 = 3$

STEP 4

Next, we can move the constant term from the left side to the right side by adding $13$ to both sides of the equation.
$2u - 13 + 13 = 3 + 13$

STEP 5

Combine the constant terms on the right side of the equation.
$2u = 16$

STEP 6

Now, we need to isolate $u$ by dividing both sides of the equation by the coefficient of $u$ , which is $2$ .
$\frac{2u}{2} = \frac{16}{2}$

STEP 7

Simplify both sides of the equation to find the value of $u$ .
$u = 8$

STEP 8

The solution set for the equation is the set containing the value of $u$ that satisfies the equation.
$\text{The solution set is } \{8\}.$

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Solve the equation −6u−13=3−8u-6u-13=3-8u−6u−13=3−8u. The solution set is {u}\{u\}{u}.

STEP 1

Assumptions1. We are given the linear equation −6u−13=3−8u-6u - 13 = 3 - 8u−6u−13=3−8u.2. We need to solve for the variable uuu.3. The solution set will be in the form {u}\{u\}{u} where uuu is the value that satisfies the equation.

STEP 2

To solve for uuu, we need to isolate the variable on one side of the equation. First, we can move all terms involving uuu to one side of the equation by adding 8u8u8u to both sides.−6u−13+8u=3−8u+8u-6u - 13 + 8u = 3 - 8u + 8u−6u−13+8u=3−8u+8u

STEP 3

Combine like terms on both sides of the equation.2u−13=32u - 13 = 32u−13=3

STEP 4

Next, we can move the constant term from the left side to the right side by adding 131313 to both sides of the equation.2u−13+13=3+132u - 13 + 13 = 3 + 132u−13+13=3+13

STEP 5

Combine the constant terms on the right side of the equation.2u=162u = 162u=16

STEP 6

Now, we need to isolate uuu by dividing both sides of the equation by the coefficient of uuu, which is 222.2u2=162\frac{2u}{2} = \frac{16}{2}22u​=216​

STEP 7

Simplify both sides of the equation to find the value of uuu.u=8u = 8u=8

STEP 8

The solution set for the equation is the set containing the value of uuu that satisfies the equation.The solution set is {8}.\text{The solution set is } \{8\}.The solution set is {8}.

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

Solve the equation $-6u-13=3-8u$ . The solution set is $\{u\}$ .

Assumptions
1. We are given the linear equation $-6u - 13 = 3 - 8u$ .
2. We need to solve for the variable $u$ .
3. The solution set will be in the form $\{u\}$ where $u$ is the value that satisfies the equation.

To solve for $u$ , we need to isolate the variable on one side of the equation. First, we can move all terms involving $u$ to one side of the equation by adding $8u$ to both sides.
$-6u - 13 + 8u = 3 - 8u + 8u$

Combine like terms on both sides of the equation.
$2u - 13 = 3$

Next, we can move the constant term from the left side to the right side by adding $13$ to both sides of the equation.
$2u - 13 + 13 = 3 + 13$

Combine the constant terms on the right side of the equation.
$2u = 16$

Now, we need to isolate $u$ by dividing both sides of the equation by the coefficient of $u$ , which is $2$ .
$\frac{2u}{2} = \frac{16}{2}$

Simplify both sides of the equation to find the value of $u$ .
$u = 8$

The solution set for the equation is the set containing the value of $u$ that satisfies the equation.
$\text{The solution set is } \{8\}.$