Questions: Solve for (u). (-5 u-8=-2 u-1+4 u) (u=)

Transcript text: Solve for $u$. \[ \begin{array}{l} -5 u-8=-2 u-1+4 u \\ u=\square \end{array} \]

Solution

Solution Steps

To solve for $ u $, we need to simplify and combine like terms on both sides of the equation. Then, isolate $ u $ by performing algebraic operations such as addition, subtraction, multiplication, or division as necessary.

Step 1: Simplify and Combine Like Terms

Start with the given equation: \[ -5u - 8 = -2u - 1 + 4u \]

Combine like terms on the right side: \[ -5u - 8 = 2u - 1 \]

Step 2: Isolate the Variable

To isolate $ u $, add $ 5u $ to both sides of the equation: \[ -8 = 7u - 1 \]

Next, add 1 to both sides to further isolate the term with $ u $: \[ -8 + 1 = 7u \]

Simplify the left side: \[ -7 = 7u \]

Step 3: Solve for $ u $

Divide both sides by 7 to solve for $ u $: \[ u = \frac{-7}{7} \]

Simplify the fraction: \[ u = -1 \]

Final Answer

$\boxed{u = -1}$

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