Complete the process of solving the equation.

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
9(u+8)–10=4u+7
9u+72–10=4u+7
Add 9 to both sides
Subtract 9 from both sides
Multiply both sides by 9
Divide both sides by 9
Apply the distributive property
9u+
=4u+7
Combine like terms
5u+62=7
Add 4u to both sides
Subtract 4u from both sides
Multiply both sides by 4u
Divide both sides by 4u
Apply the distributive property
5u=

55
Add 62 to both sides
Subtract 62 from both sides
Multiply both sides by 62
Divide both sides by 62
Apply the distributive property
u=
Divide both sides by 5

1 answer

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: \[ 9(u + 8) - 10 = 4u + 7 \]

  1. Apply the distributive property: \[ 9u + 72 - 10 = 4u + 7 \]

  2. Combine like terms (on the left side): \[ 9u + 62 = 4u + 7 \]

  3. Subtract \(4u\) from both sides: \[ 9u - 4u + 62 = 7 \] Which simplifies to: \[ 5u + 62 = 7 \]

  4. Subtract \(62\) from both sides: \[ 5u = 7 - 62 \] Which simplifies to: \[ 5u = -55 \]

  5. 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 \(5\): \(u = -11\)