solving rational equation?

Question

solve.

-5√8x-4 +3 = 18

how do i find the answer to this one? what are the steps?
the 8x-4 are under the square root, not the +3.

Answer 1

This does not have a solution.
The reason is though each number has 2 square root sqrt(a) is taken to be positive square root.

Answer 2

Given the equation -5 sqrt (8x - 4) + 3 = 18. To solve for x, 3 is transposed to the right hand side of the equation. That is:
-5 sqrt (8x - 4) = 18 - 3
-5 sqrt (8x - 4) = 15.

This equation reduces to sqrt (8x - 4) = -3. Then, 4 is factored out in the expression 8x - 4. So
sqrt (4[2x - 1] ) = -3
2 sqrt (2x - 1) = -3.

Squaring both sides of the previous equation gives the following:
4 (2 x - 1) = 9
4(2 x) - 4(1) = 9
8 x - 4 = 9.

Transposing 4 to the right hand side of the previous equation gives
8 x = 9 + 4
8 x = 13.

By dividing both sides of the previous equation by 8 will yield to
x = 13 / 8.

Now, this value of x is plugged to the given equation to determine if it is the solution or the extraneous root of the given equation. That is, on the left-hand side of the given equation:
-5 (sqrt ( 8[13/8] - 4) + 3
= -5 sqrt ( 13 - 4 ) + 3
= -5 sqrt ( 9 ) + 3
= -5(3) + 3
= - 15 + 3
= - 12.

Unfortunately, -12 < 18 and is NOT equal to the value in the right-hand side, 18. Thus, the root x = 13 / 8 is an extraneous root of the given equation. So, there is NO SOLUTION for the given equation. That is, the SOLUTION SET (for x) is the EMPTY SET.

Answer 3

-5√(8x - 4) + 3 = 18

The goal is to get the x alone. In order to do that, you need to...
Minus 3 from both sides of the equation.

-5√(8x - 4) + 3 - 3 = 18 - 3; -5√(8x - 4) = 15

Then you need to get rid of the -5. To do that you need to divide both sides.

(-5√(8x - 4)) / -5 = 15 / -5; √(8x - 4) = -3

Now, you have a square root to take care of. In order to get rid of the square root, you need to square both sides ^2.

(√(8x - 4))^2 = -3^2; 8x - 4 = 9

Just like the first step in getting rid of the 3, we do the same with the 4.

8x - 4 + 4 = 9 + 4; 8x = 13

Now, we divide both sides by 8.

8x / 8 = 13 / 8

x = 13/8

Answer 4

first,
bring the three to the other side it will become
-5.........=18-3
-5.........=15
then,
bring the -5 to the other side
it will become root of 8x-4=15/-5
which is nothing but root of 8x-4= -3
now when u square both the sides
it will become
(root of 8x-4)raised to 2= (-3) raised to 2
then the root on 8x-4 and the raised to 2 will get canceled
and on the right hand side, square of -3 is+9
hence'
8x-4=9
8x=9+4
8x=13
x=13/8
hope the ans is right

Answer 5

-5sqrt(8x - 4) + 3 = 18

-5 sqrt(8x - 4) = 15

sqrt(8x - 4) = - 3

squaring both sides we get,

8x - 4 = 9

8x = 13

x = 13/8

Answer 6

(-5)(root 8x-4)+3=18
(-5)(root 8x-4) =18-3=15
(root 8x-4) =15/-5 =-3
Squaring both sides, 8x-4 =9
8x =9+4 =13
x =13/8 =1 5/8= 1.625

Answer 7

-5√(8x-4) +3 = 18
-5√(8x-4)=18-3=15
√(8x-4)=15/(-5)=-3 square both sides
8x-4=9
8x=13
x=13/8=1.625

check
-5√(8x-4)+3=18
-5√(8(1.625)-4)+3=18
-5√(9)+3=18
-5(+/-3)+3=18
-5(-3)+3=18 is corrrect
-5(3)+3=18 is not

Answer 8

-5sqrt(8x-4) = 18 - 3
sqrt(8x-4) = 15/-5
8x-4 = (-3)^2
8x = 9 + 4
x = 13/8

-5sqrt((8*13/8)-4) + 3 =? 18
-5sqrt(13-4) + 3 = 18
-5sqrt(9) + 3 = 18
-5*3 + 3 = 18 NOT
-5*-3 + 3 = 18

Answer 9

... 10/(x-1) + 1 = 20/(x²-1) ... x ≠ ±1 ← Else equation becomes undefined or 10/(x-1) + 1 = 20/[ (x-1)(x+1) ] or 10(x+1) + (x-1)(x+1) = 20 or 10x + 10 + x² - 1 = 20 or x² + 10x - 11 = 0 or (x - 1) (x + 11) = 0 or x = 1 ....... ← Reject due to initial constraint or x = -11 .... ← Final solution

Answer 10

-5root(8x-4)=15
root(8x-4)=-3
squaring both sides
8x-4=9
8x=13
x=13/8