Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
15(
–
6t+6)+15=18t–3
90t–90+15=18t–3
Add -15 to both sides
Subtract -15 from both sides
Multiply both sides by -15
Divide both sides by -15
Apply the distributive property
90t–75=18t–3
Add -90 to both sides
Subtract -90 from both sides
Multiply both sides by -90
Divide both sides by -90
Combine like terms
–75=
–
3 Subtract 18t from both sides
72t=
Add 75 to both sides
t=
Divide both sides by 72

Answer 1

Let's complete the process of solving the equation step by step, filling in the missing terms and descriptions as needed.

1. Starting with the original equation: \[ -15(-6t + 6) + 15 = 18t - 3 \]

2. Apply the distributive property: \[ -15(-6t) + (-15)(6) + 15 = 18t - 3 \] This simplifies to: \[ 90t - 90 + 15 = 18t - 3 \]

3. Combine like terms on the left side: \[ 90t - 75 = 18t - 3 \]

4. Subtract \(18t\) from both sides: \[ 90t - 18t - 75 = -3 \] This simplifies to: \[ 72t - 75 = -3 \]

5. Add \(75\) to both sides: \[ 72t = -3 + 75 \] Thus: \[ 72t = 72 \]

6. Divide both sides by \(72\): \[ t = \frac{72}{72} \] Therefore: \[ t = 1 \]

Summary of Steps:

• Original Equation: \( -15(-6t + 6) + 15 = 18t - 3 \)
• Apply the distributive property.
• Combine like terms: \( 90t - 75 = 18t - 3 \)
• Subtract \( 18t \) from both sides.
• Add \( 75 \) to both sides.
• Divide by \( 72 \): \( t = 1 \)

Missed Terms and Descriptions:

• Apply the distributive property
• Combine like terms
• Subtract \( 18t \) from both sides
• Add \( 75 \) to both sides
• Divide both sides by \( 72 \)

Final solution: \[ t = 1 \]