Question

Solve.

Start Fraction 1 over 2 x minus 8 End Fraction minus Start Fraction 3 over x minus 4 End Fraction equals negative 5

Answer 1

try again and see if it could be 3, 9/2, 6, -24/5

Answer 2

use 3, 9/2, 6, -24/5 each and replace x to see if they will result in the same answer

Answer 3

1/(2x - 8) - 3/(x - 4) = -5

To solve this equation, first find a common denominator between 2x - 8 and x - 4, which is (2x - 8)(x - 4) or 2(x - 4). Multiply each fraction by the missing factor in its denominator:

[(x - 4)/(x - 4)]/(2x - 8) - [3(2)/(2x - 8)]/(x - 4) = -5

Simplify:

(x - 4)/2(2x - 8) - 6/(2x - 8) = -5

Then, combine the fractions into a single fraction:

(x - 4 - 6)/2(2x - 8) = -5

Simplify:

(x - 10)/4(2x - 8) = -5

Now, multiply both sides by 4(2x - 8):

4(x - 10) = -20(2x - 8)

Expand the equation:

4x - 40 = -40x + 160

Combine like terms:

44x = 200

Finally, find the value of x:

x = 200 / 44

x = 100 / 22

x = 50 / 11

Therefore, the solution to the equation 1/(2x - 8) - 3/(x - 4) = -5 is x = 50/11.

Answer 4

Let's solve the equation again:

1/(2x - 8) - 3/(x - 4) = -5

First, find a common denominator between the two fractions:

2(x - 4) and (2x - 8)

Now, the equation becomes:

(x - 4)/(2(x - 4)) - 6/(2(x - 4)) = -5

Combine the fractions:

(x - 4 - 6)/(2(x - 4)) = -5

Simplify:

(x - 10)/(2x - 8) = -5

Cross multiply:

(x - 10) = -5(2x - 8)
x - 10 = -10x + 40

Add 10x to both sides:

11x - 10 = 40

Add 10 to both sides:

11x = 50

Divide by 11:

x = 50/11

The possible solutions are x = 50/11, which confirms the solution you provided. Therefore, the potential solutions for the equation 1/(2x - 8) - 3/(x - 4) = -5 are x = 50/11.

Answer 5

Let's substitute each potential solution into the original equation and see which one results in the correct answer of -5.

1. Substitute x = 3:

1/(2*3 - 8) - 3/(3 - 4)
= 1/(6 - 8) - 3/(3 - 4)
= 1/(-2) - 3/(-1)
= -1/2 + 3
= 5/2

Since the above result is not -5, x = 3 is not a solution.

2. Substitute x = 9/2:

1/(2*(9/2) - 8) - 3/(9/2 - 4)
= 1/(9 - 8) - 3/(4.5 - 4)
= 1/1 - 3/0.5
= 1 - 6
= -5

So, x = 9/2 is a solution.

3. Substitute x = 6:

1/(2*6 - 8) - 3/(6 - 4)
= 1/(12 - 8) - 3/(6 - 4)
= 1/4 - 3/2
= 1/4 - 6/4
= -5/4

Since the above result is not -5, x = 6 is not a solution.

4. Substitute x = -24/5:

1/(2*(-24/5) - 8) - 3/(-24/5 - 4)
= 1/((-48/5) - 8) - 3/( -24/5 - 4)
= 1/(-48/5 - 40/5) - 3/(-24/5 - 20/5)
= 1/(-88/5) - 3/(-44/5)
= -5 - 15
= -20

Since the above result is not -5, x = -24/5 is not a solution.

Therefore, the only solution that resulted in -5 when substituted back into the original equation is x = 9/2.