Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -7u - 10 - 2u = -8u + 12 -9u - 10 = -8u + 12 -u - 10 = 12 -u = add 10 to both sides u = divide both sides by -1

Explanation:

Step1: Identify first operation

To get from \(-7u - 10 - 2u\) to \(-9u - 10\), we combine like terms (the \(u\)-terms). So the first missing description is "Combine like terms".

Step2: Identify second operation

To get from \(-9u - 10 = -8u + 12\) to \(-u - 10 = 12\), we add \(8u\) to both sides (or add \(9u\) to both sides, but adding \(8u\) to both sides: \(-9u + 8u - 10 = -8u + 8u + 12\) simplifies to \(-u - 10 = 12\)). So the second missing description is "Add \(8u\) to both sides" (or "Add \(9u\) to both sides", but adding \(8u\) is more direct here).

Step3: Solve for \(-u\)

We have \(-u - 10 = 12\). Using the operation "Add 10 to both sides", we add 10 to each side: \(-u - 10 + 10 = 12 + 10\), so \(-u = 22\).

Step4: Solve for \(u\)

Using the operation "Divide both sides by \(-1\)", we divide \(-u = 22\) by \(-1\): \(u = \frac{22}{-1} = -22\).

Answer:

First missing description: Combine like terms
Second missing description: Add \(8u\) to both sides (or similar valid operation)
\(-u = \boldsymbol{22}\)
\(u = \boldsymbol{-22}\)

(For the dropdowns: first dropdown: "Combine like terms", second dropdown: "Add 8u to both sides" (or equivalent), then the boxes: 22 and -22)