Question

solve the equation, if possible. check the result. (if there is no solution, enter no solution. if
\\(\frac{2(6 - u)}{3} = -2u + 6\\)
enter a fraction, integer, or exact decimal. do not approximate.
learn it: solve linear equations in one variable that require simplifying one or both
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Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation $\frac{2(6 - u)}{3} = -2u + 6$ by 3 to get rid of the fraction.
$$3\times\frac{2(6 - u)}{3}=3\times(-2u + 6)$$
Simplifying both sides, we have $2(6 - u)=-6u + 18$.

Step2: Expand the left - hand side

Use the distributive property $a(b - c)=ab - ac$ to expand $2(6 - u)$.
$2\times6-2\times u=-6u + 18$, which simplifies to $12-2u=-6u + 18$.

Step3: Move the terms with u to one side

Add $6u$ to both sides of the equation $12-2u=-6u + 18$.
$12-2u + 6u=-6u + 18+6u$, which simplifies to $12 + 4u=18$.

Step4: Solve for u

Subtract 12 from both sides: $12 + 4u-12=18 - 12$.
Simplifying, we get $4u = 6$.
Then divide both sides by 4: $u=\frac{6}{4}=\frac{3}{2}$.

Answer:

$\frac{3}{2}$