Using the equality properties, we can solve the problem 3/2 (4-8x) + 5x = 1 - 7x as follows:
1. Divide the 3/2 among the terms enclosed in parenthesis as follows:
(3/2)(4) - (3/2)(8x) + 5x = 1 - 7x
That amounts to:
6 - 12x/2 + 5x = 1 - 7x
2. Clarify the terminology on the left:
6 - 6x + 5x = 1 - 7x
combining similar terms
6 - x = 1 - 7x
3. Isolate x on one side to remove the variables:
X-terms should be moved to the left:
-x + 7x = 1 - 6
combining similar terms
6x = -5
4. By dividing both sides by 6, find the value of x:
x = -5/6
As a result, the equation's answer is x = -5/6.
There is only one solution because we determined a certain value for x.
Correct! The equation has one solution since we found a specific value for x, which is x = -5/6.
That is correct! The solution to the equation is indeed x = -5/6. Well done!
To solve the given equation using the equality properties, you followed a step-by-step process. Here is a breakdown of each step:
1. Divide the 3/2 among the terms enclosed in parentheses:
You distributed 3/2 to both 4 and -8x, resulting in (3/2)(4) - (3/2)(8x) + 5x = 1 - 7x.
2. Simplify the terms on the left:
By performing the multiplication, you obtained 6 - 12x/2 + 5x = 1 - 7x.
3. Combine similar terms on the left side:
You simplified further by combining the terms -12x/2 and 5x, resulting in 6 - x = 1 - 7x.
4. Isolate x on one side:
To isolate the x terms, you moved the -x and -7x to the left side by adding x to both sides, resulting in -x + 7x = 1 - 6.
5. Combine similar terms:
On the left side, you combined -x and 7x to get 6x. On the right side, you combined 1 and -6 to get -5, resulting in 6x = -5.
6. Solve for x:
By dividing both sides of the equation by 6, you obtained x = -5/6.
Therefore, the solution to the equation is x = -5/6. The equation has only one solution because you found a specific value for x that satisfies the equation.