use the distributive property to solve the equation 3(x - 7) = 2x + 4 for x.
1.
3(x - 7) = 2x + 4
(______)(x) + (______)(-7) = 2x + 4
______x - ______ = 2x + 4
______x - ______ - ______ = 2x + 4 - ______
______ - ______ = 4
______ - ______ + ______ = 4 + ______
x = ______
multiply both terms inside the parentheses by 3.
combine like terms.
subtract 2x from both sides.
add 21 to both sides.
2. the solution is x = ______.
3. check. substitute the solution into the equation for x.
3(x - 7) = 2x + 4
3(______ - 7) = 2(______) + 4
3(______) = ______ + 4
______ = ______
solve 2(x + 40 + 7x) = 4x + 20 for x.
4.
2(x + 40 + 7x) = 4x + 20
2(______x + 40) = 4x + 20
2(______x) + 2(______) = 4x + 20
______x + ______ = 4x + 20
16x + 80 - ______x = 4x + 20 - ______x
______x + 80 - ______ = 20 - ______
______x = ______
x = ______
combine like terms inside the parentheses.
use the distributive property.
subtract 4x from both sides.
subtract 80 from both sides.
divide both sides by 12.
5. the solution is x = ______.

Question

Accepted Answer

### Solving $ 3(x - 7) = 2x + 4 $

#### Step 1: Apply Distributive Property
The distributive property states $ a(b + c) = ab + ac $. For $ 3(x - 7) $, we multiply 3 by $ x $ and 3 by $ -7 $:
$ (3)(x) + (3)(-7) = 2x + 4 $

#### Step 2: Simplify the Left Side
Multiply the terms:
$ 3x - 21 = 2x + 4 $

#### Step 3: Subtract $ 2x $ from Both Sides
To isolate $ x $-terms, subtract $ 2x $ from both sides:
$ 3x - 21 - 2x = 2x + 4 - 2x $

#### Step 4: Combine Like Terms
Simplify both sides:
$ x - 21 = 4 $

#### Step 5: Add 21 to Both Sides
To solve for $ x $, add 21 to both sides:
$ x - 21 + 21 = 4 + 21 $

#### Step 6: Final Solution
Simplify:
$ x = 25 $

### Checking the Solution
Substitute $ x = 25 $ into the original equation $ 3(x - 7) = 2x + 4 $:

1. Left side: $ 3(25 - 7) = 3(18) = 54 $
2. Right side: $ 2(25) + 4 = 50 + 4 = 54 $

Both sides are equal, so $ x = 25 $ is correct.

### Solving $ 2(x + 40 + 7x) = 4x + 20 $

#### Step 1: Combine Like Terms Inside Parentheses
Combine $ x $ and $ 7x $:
$ 2(8x + 40) = 4x + 20 $

#### Step 2: Apply Distributive Property
Multiply 2 by $ 8x $ and 2 by $ 40 $:
$ 2(8x) + 2(40) = 4x + 20 $

#### Step 3: Simplify the Left Side
Multiply the terms:
$ 16x + 80 = 4x + 20 $

#### Step 4: Subtract $ 4x $ from Both Sides
Isolate $ x $-terms:
$ 16x + 80 - 4x = 4x + 20 - 4x $

#### Step 5: Combine Like Terms
Simplify both sides:
$ 12x + 80 = 20 $

#### Step 6: Subtract 80 from Both Sides
Isolate the $ x $-term:
$ 12x + 80 - 80 = 20 - 80 $

#### Step 7: Simplify
$ 12x = -60 $

#### Step 8: Divide by 12
Solve for $ x $:
$ x = \frac{-60}{12} = -5 $

### Final Answers
1. For $ 3(x - 7) = 2x + 4 $:
   - Distributive step: $ 3, 3 $
   - Simplified: $ 3x - 21 $
   - Subtract $ 2x $: $ 3x - 21 - 2x = 2x + 4 - 2x $
   - Combine terms: $ x - 21 = 4 $
   - Add 21: $ x - 21 + 21 = 4 + 21 $
   - Solution: $ \boldsymbol{x = 25} $

2. For $ 2(x + 40 + 7x) = 4x + 20 $:
   - Combine like terms: $ 8x $
   - Distributive step: $ 8x, 40 $
   - Simplified: $ 16x + 80 $
   - Subtract $ 4x $: $ 16x + 80 - 4x = 4x + 20 - 4x $
   - Combine terms: $ 12x + 80 = 20 $
   - Subtract 80: $ 12x = -60 $
   - Divide: $ x = -5 $
   - Solution: $ \boldsymbol{x = -5} $

QUESTION IMAGE

Question

Explanation:

Solving \( 3(x - 7) = 2x + 4 \)

Step 1: Apply Distributive Property

Step 2: Simplify the Left Side

Step 3: Subtract \( 2x \) from Both Sides

Step 4: Combine Like Terms

Step 5: Add 21 to Both Sides

Step 6: Final Solution

Checking the Solution

Solving \( 2(x + 40 + 7x) = 4x + 20 \)

Step 1: Combine Like Terms Inside Parentheses

Step 2: Apply Distributive Property

Step 3: Simplify the Left Side

Step 4: Subtract \( 4x \) from Both Sides

Step 5: Combine Like Terms

Step 6: Subtract 80 from Both Sides

Step 7: Simplify

Step 8: Divide by 12

Final Answers

Answer: