Solved on Jan 29, 2024

Solve for $u$ in the equation $-5(u+2)=u-2+2(3u+3)$ . Simplify the solution $u=$ .

STEP 1

Assumptions
1. We are given the equation $-5(u+2)=u-2+2(3u+3)$ .
2. We need to solve for the variable $u$ .

STEP 2

Distribute the $-5$ across the terms inside the parentheses on the left-hand side of the equation.
$-5(u+2) = -5u - 10$

STEP 3

Distribute the $2$ across the terms inside the parentheses on the right-hand side of the equation.
$2(3u+3) = 6u + 6$

STEP 4

Rewrite the original equation with the distributed terms.
$-5u - 10 = u - 2 + 6u + 6$

STEP 5

Combine like terms on the right-hand side of the equation.
$-5u - 10 = 7u + 4$

STEP 6

Add $5u$ to both sides of the equation to get all the $u$ terms on one side.
$-5u + 5u - 10 = 7u + 5u + 4$

STEP 7

Simplify both sides of the equation after adding $5u$ .
$-10 = 12u + 4$

STEP 8

Subtract $4$ from both sides of the equation to isolate the term with $u$ on one side.
$-10 - 4 = 12u + 4 - 4$

STEP 9

Simplify both sides of the equation after subtracting $4$ .
$-14 = 12u$

STEP 10

Divide both sides of the equation by $12$ to solve for $u$ .
$\frac{-14}{12} = \frac{12u}{12}$

STEP 11

Simplify both sides of the equation after dividing by $12$ .
$u = \frac{-14}{12}$

STEP 12

Reduce the fraction $\frac{-14}{12}$ to its simplest form.
$u = \frac{-7}{6}$
The solution for $u$ is: $u = \frac{-7}{6}$

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Solve for $u$ in the equation $-5(u+2)=u-2+2(3u+3)$ . Simplify the solution $u=$ .

STEP 1

Assumptions
1. We are given the equation $-5(u+2)=u-2+2(3u+3)$ .
2. We need to solve for the variable $u$ .

STEP 2

Distribute the $-5$ across the terms inside the parentheses on the left-hand side of the equation.
$-5(u+2) = -5u - 10$

STEP 3

Distribute the $2$ across the terms inside the parentheses on the right-hand side of the equation.
$2(3u+3) = 6u + 6$

STEP 4

Rewrite the original equation with the distributed terms.
$-5u - 10 = u - 2 + 6u + 6$

STEP 5

Combine like terms on the right-hand side of the equation.
$-5u - 10 = 7u + 4$

STEP 6

Add $5u$ to both sides of the equation to get all the $u$ terms on one side.
$-5u + 5u - 10 = 7u + 5u + 4$

STEP 7

Simplify both sides of the equation after adding $5u$ .
$-10 = 12u + 4$

STEP 8

Subtract $4$ from both sides of the equation to isolate the term with $u$ on one side.
$-10 - 4 = 12u + 4 - 4$

STEP 9

Simplify both sides of the equation after subtracting $4$ .
$-14 = 12u$

STEP 10

Divide both sides of the equation by $12$ to solve for $u$ .
$\frac{-14}{12} = \frac{12u}{12}$

STEP 11

Simplify both sides of the equation after dividing by $12$ .
$u = \frac{-14}{12}$

STEP 12

Reduce the fraction $\frac{-14}{12}$ to its simplest form.
$u = \frac{-7}{6}$
The solution for $u$ is: $u = \frac{-7}{6}$

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Solve for uuu in the equation −5(u+2)=u−2+2(3u+3)-5(u+2)=u-2+2(3u+3)−5(u+2)=u−2+2(3u+3). Simplify the solution u=u=u=.

STEP 1

Assumptions1. We are given the equation −5(u+2)=u−2+2(3u+3)-5(u+2)=u-2+2(3u+3)−5(u+2)=u−2+2(3u+3).2. We need to solve for the variable uuu.

STEP 2

Distribute the −5-5−5 across the terms inside the parentheses on the left-hand side of the equation.−5(u+2)=−5u−10-5(u+2) = -5u - 10−5(u+2)=−5u−10

STEP 3

Distribute the 222 across the terms inside the parentheses on the right-hand side of the equation.2(3u+3)=6u+62(3u+3) = 6u + 62(3u+3)=6u+6

STEP 4

Rewrite the original equation with the distributed terms.−5u−10=u−2+6u+6-5u - 10 = u - 2 + 6u + 6−5u−10=u−2+6u+6

STEP 5

Combine like terms on the right-hand side of the equation.−5u−10=7u+4-5u - 10 = 7u + 4−5u−10=7u+4

STEP 6

Add 5u5u5u to both sides of the equation to get all the uuu terms on one side.−5u+5u−10=7u+5u+4-5u + 5u - 10 = 7u + 5u + 4−5u+5u−10=7u+5u+4

STEP 7

Simplify both sides of the equation after adding 5u5u5u.−10=12u+4-10 = 12u + 4−10=12u+4

STEP 8

Subtract 444 from both sides of the equation to isolate the term with uuu on one side.−10−4=12u+4−4-10 - 4 = 12u + 4 - 4−10−4=12u+4−4

STEP 9

Simplify both sides of the equation after subtracting 444.−14=12u-14 = 12u−14=12u

STEP 10

Divide both sides of the equation by 121212 to solve for uuu.−1412=12u12\frac{-14}{12} = \frac{12u}{12}12−14​=1212u​

STEP 11

Simplify both sides of the equation after dividing by 121212.u=−1412u = \frac{-14}{12}u=12−14​

STEP 12

Reduce the fraction −1412\frac{-14}{12}12−14​ to its simplest form.u=−76u = \frac{-7}{6}u=6−7​The solution for uuu is: u=−76 u = \frac{-7}{6} u=6−7​

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

Solve for $u$ in the equation $-5(u+2)=u-2+2(3u+3)$ . Simplify the solution $u=$ .

Assumptions
1. We are given the equation $-5(u+2)=u-2+2(3u+3)$ .
2. We need to solve for the variable $u$ .

Distribute the $-5$ across the terms inside the parentheses on the left-hand side of the equation.
$-5(u+2) = -5u - 10$

Distribute the $2$ across the terms inside the parentheses on the right-hand side of the equation.
$2(3u+3) = 6u + 6$

Rewrite the original equation with the distributed terms.
$-5u - 10 = u - 2 + 6u + 6$

Combine like terms on the right-hand side of the equation.
$-5u - 10 = 7u + 4$

Add $5u$ to both sides of the equation to get all the $u$ terms on one side.
$-5u + 5u - 10 = 7u + 5u + 4$

Simplify both sides of the equation after adding $5u$ .
$-10 = 12u + 4$

Subtract $4$ from both sides of the equation to isolate the term with $u$ on one side.
$-10 - 4 = 12u + 4 - 4$

Simplify both sides of the equation after subtracting $4$ .
$-14 = 12u$

Divide both sides of the equation by $12$ to solve for $u$ .
$\frac{-14}{12} = \frac{12u}{12}$

Simplify both sides of the equation after dividing by $12$ .
$u = \frac{-14}{12}$

Reduce the fraction $\frac{-14}{12}$ to its simplest form.
$u = \frac{-7}{6}$
The solution for $u$ is: $u = \frac{-7}{6}$