Question

Solve the equation for x. do not include "x=" in your answer. 12 √1 - 5x = 18

a. -6/5
b. 6/5
c. 5/6
d. -5/6

Answer 1

To solve the equation, we isolate the square root, square both sides, rearrange to solve for x, and divide by the coefficient of x. This results in x being -0.25, which doesn't match any of the provided multiple-choice answers, indicating a possible discrepancy in the original question.

Step-by-step explanation:

To solve the equation 12 √(1 - 5x) = 18 for x, we begin by isolating the square root on one side of the equation. We do this by dividing both sides by 12:

√(1 - 5x) = 1.5

We then square both sides to remove the square root:

(√(1 - 5x))^2 = (1.5)^2

1 - 5x = 2.25

Next, we rearrange the equation to solve for x:

-5x = 2.25 - 1

-5x = 1.25

Now, we divide both sides by -5:

x = 1.25 / -5

x = -0.25

This answer is not explicitly listed in the multiple-choice options provided, potentially due to a confusion in the original question or a typo. However, the process for solving the equation is demonstrated step by step.

Answer 2

The solution to the equation 12√1 - 5x = 18 is x = 5/6. Option C is answer.

Step-by-step explanation:

First, we subtract 18 from both sides of the equation to get:

12√1 - 5x - 18 = 0

Now, we square both sides of the equation to eliminate the radical:

(12√1 - 5x)^2 = 0

Expanding both sides, we get:

144 - 144√1 + 25x^2 = 0

Combining like terms, we get:

25x^2 - 144√1 + 144 = 0

To solve for x, we need to rearrange the equation so that x is isolated on one side of the equal sign. We can do this by subtracting 144 from both sides:

25x^2 - 144√1 = -144

Now, we divide both sides by 25:

x^2 - 5√1 = -5.6

Adding 5√1 to both sides, we get:

x^2 = 5√1 - 5.6

Taking the square root of both sides, we get:

x = ±√(5√1 - 5.6)

Since the left side of the equation is non-negative, we know that the solution must be the positive root:

x = √(5√1 - 5.6)

Finally, we simplify the expression under the radical:

x = √(5√1 - 5.6) ≈ 5/6

Option C is answer.