Question

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

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.
\(3\times\frac{2(6 - u)}{3}=3\times(-2u + 6)\)
Simplify both sides: \(2(6 - u)=-6u + 18\)

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:
\(12-2u + 6u=-6u + 18+6u\)
Simplify: \(12 + 4u=18\)

Step4: Solve for \(u\)

Subtract 12 from both sides:
\(12 + 4u-12=18-12\)
Simplify: \(4u = 6\)
Divide both sides by 4:
\(u=\frac{6}{4}=\frac{3}{2}\)

Answer:

\(u = \frac{3}{2}\)