4(2x + 3) = 2(3x - 4)


one solution
infinite solutions * my answer*
no solution

6 - a = 1/3(9a - 18)
one solution * my answer*
infinite solutions
no solution

3(4x - 3) - 7x = 5x - 9
one solution
infinite solutions *my answer*
no solution

4(2x - 3) - 4x (answer all that apply)

4x – 12 *my answer*
3x – 4

3(2x – 6) *my answer*

4(x – 5)

4(2x + 3) = 2(3x - 4)

8x+12 = 6x-8
2x = -20
x = -10
Bzzzt

6 - a = 1/3(9a - 18)
18-3a = 9a-18
12a = 36
a = 3
correct

3(4x - 3) - 7x = 5x - 9
12x-9-7x = 5x-9
5x-9 = 5x-9
correct - the same line

4(2x - 3) - 4x
8x-12-4x
4x-12
2(2x-6)
4(x-3)
only your first choice is correct

Is it correct

To solve the given equations, we will simplify and apply the appropriate algebraic operations.

1. 4(2x + 3) = 2(3x - 4)

First, distribute the constants within the parentheses:
8x + 12 = 6x - 8

Next, combine like terms by subtracting 6x from both sides and subtracting 12 from both sides:
8x - 6x = -8 - 12

Simplify:
2x = -20

Finally, divide both sides of the equation by 2 to solve for x:
x = -10

Since there is one solution, the correct answer is "one solution."

2. 6 - a = 1/3(9a - 18)

First, distribute the 1/3 to the terms within the parentheses:
6 - a = (1/3) * 9a - (1/3) * 18

Simplify:
6 - a = 3a - 6

Next, add 'a' to both sides and add 6 to both sides:
6 + 6 = 3a + a

Simplify:
12 = 4a

Finally, divide both sides of the equation by 4 to find the value of 'a':
a = 3

Since there is one solution, the correct answer is "one solution."

3. 3(4x - 3) - 7x = 5x - 9

First, distribute the constants within the parentheses:
12x - 9 - 7x = 5x - 9

Next, combine like terms by subtracting 5x from both sides and adding 9 to both sides:
12x - 7x - 5x = -9 + 9

Simplify:
0 = 0

No matter what value we assign to 'x', the equation will always be true. Therefore, there are infinite solutions.

The correct answer is "infinite solutions."

4. 4(2x - 3) - 4x

First, distribute the constant 4 to the terms within the parentheses:
8x - 12 - 4x

Combine like terms:
8x - 4x - 12

Simplify:
4x - 12

The equation has been simplified, and no specific solution has been determined. Therefore, we cannot definitively state that there is no solution.

The correct answer is "4x - 12."

5. 3(2x - 6)

First, distribute the constant 3 to the terms within the parentheses:
6x - 18

The equation has been simplified, and no specific solution has been determined. Therefore, we cannot definitively state that there is no solution.

The correct answer is "6x - 18."

6. 4(x - 5)

First, distribute the constant 4 to the terms within the parentheses:
4x - 20

The equation has been simplified, and no specific solution has been determined. Therefore, we cannot definitively state that there is no solution.

The correct answer is "4x - 20."

To solve the equations, let's go step by step:

1. 4(2x + 3) = 2(3x - 4)
First, distribute the numbers outside the brackets:
8x + 12 = 6x - 8
Next, move all the variable terms to one side and the constant terms to the other side:
8x - 6x = -8 - 12
Simplifying the equation:
2x = -20
Finally, divide both sides of the equation by 2 to isolate the variable:
x = -10

2. 6 - a = 1/3(9a - 18)
Let's distribute the fraction:
6 - a = (9a - 18) / 3
Next, simplify the right side of the equation:
6 - a = 3a - 6
Move all the variable terms to one side and the constant terms to the other side:
-a - 3a = -6 - 6
Simplifying the equation:
-4a = -12
Finally, divide both sides of the equation by -4 to solve for the variable:
a = 3

3. 3(4x - 3) - 7x = 5x - 9
Starting with the left side of the equation, apply the distributive property:
12x - 9 - 7x = 5x - 9
Combine like terms:
5x - 9 = 5x - 9
The resulting equation is 5x - 9 = 5x - 9, which means the variable cancels out and both sides are equal. Therefore, this equation has infinite solutions.

4. 4(2x - 3) - 4x (answer all that apply)
Applying the distributive property on the first term:
8x - 12 - 4x
Combine like terms:
4x - 12
So the answer is 4x – 12.

5. 3(2x - 6)
Applying the distributive property on the term:
6x - 18
Thus, the answer is 6x - 18.

6. 4(x - 5)
Applying the distributive property on the term:
4x - 20
Thus, the answer is 4x - 20.