Let's solve the equation step by step, filling in the missing terms and making sure to simplify any fractions.
We start with the given equation: \[ 9(u + 8) - 10 = 4u + 7 \]
-
Apply the distributive property: \[ 9u + 72 - 10 = 4u + 7 \]
-
Combine like terms (on the left side): \[ 9u + 62 = 4u + 7 \]
-
Subtract \(4u\) from both sides: \[ 9u - 4u + 62 = 7 \] Which simplifies to: \[ 5u + 62 = 7 \]
-
Subtract \(62\) from both sides: \[ 5u = 7 - 62 \] Which simplifies to: \[ 5u = -55 \]
-
Divide both sides by 5: \[ u = \frac{-55}{5} \] Which simplifies to: \[ u = -11 \]
Here are the missing terms and descriptions to fill in the steps:
Missing terms:
- After "9u +": 62
- After "5u =": −55
- After "u =": −11
Missing descriptions:
- After "Combine like terms": This step has already been filled in because we combined like terms in the transition to \(5u + 62 = 7\).
- The operations leading to \(5u = -55\) include Subtract 62 from both sides.
- The final operation to solve for \(u\) involves Divide both sides by 5.
Summary of the completed process:
- Start with \(9(u + 8) - 10 = 4u + 7\)
- Apply the distributive property to get \(9u + 62 = 4u + 7\)
- Subtract \(4u\) from both sides: \(5u + 62 = 7\)
- Subtract \(62\) from both sides: \(5u = -55\)
- Divide by \(5\): \(u = -11\)