Question

Solve for u.-3(2u-7)+3u=6(u+1)Simplify your answer as much as possible.

Answer 1

Given

`-3\mleft(2u-7\mright)+3u=6\mleft(u+1\mright)`

To solve for u you have to isolate the variable on one side of the expression and pass all other terms to the other side.

The first step is to solve the multiplications on both parentheses terms by applying the distributive property of multiplication. This means that you have to multiply each term inside the parentheses by the multiplier:

`\begin{gathered} -3(2u-7)+3u=6(u+1) \\ (-3)\cdot2u+(-3)(-7)+3u=6\cdot u+6\cdot1 \\ -6u+21+3u=6u+6 \end{gathered}`

Order the like terms together and simplify:

`\begin{gathered} -6u+3u+21=6u+6 \\ -3u+21=6u+6 \end{gathered}`

Next, pass 21 to the right side of the expression by applying the opposite operation to both sides of the equal sign:

`\begin{gathered} -3u+21-21=6u+6-21 \\ -3u=6u-15 \end{gathered}`

Pass 6u to the left side of the expression

`\begin{gathered} -3u-6u=6u-6u-15 \\ -9u=-15 \end{gathered}`

Divide both sides by -9

`\begin{gathered} (-9u)/(-9)=(-15)/(-9) \\ u=(5)/(3) \end{gathered}`

The value of u is 5/3.