Question

Solve this equation: 1/6x-3=1/2(x+18) show or explain your reasoning

Answer 1

x = -36

Explanation:

1/6x-3 = 1/2(x+18)

1/6x-3 = 1/2x + 9

-1/3x = 12

x =-36

Now, to double check

1/6 (-36) - 3 = 1/2(-36) + 9

-6 - 3 = -18 +9

- 9 = -9

Answer 2

The solution to the equation (1/6)x - 3 = (1/2)(x + 18) is x = -36.

Explanation:

To solve the equation (1/6)x - 3 = (1/2)(x + 18), we will follow these steps:

Distribute the 1/2 to both terms inside the parentheses on the right side of the equation:

(1/6)x - 3 = (1/2)x + 9.

Let's simplify the equation by multiplying every term by the least common denominator (LCD) of 6 to eliminate the fractions:

6 * ((1/6)x) - 6 * 3 = 6 * ((1/2)x) + 6 * 9.

This simplifies to:

x - 18 = 3x + 54.

Now, we will gather the x terms on one side of the equation and the constant terms on the other side. Subtract 3x from both sides and add 18 to both sides:

x - 3x = 54 + 18.

Simplifying further, we get:

-2x = 72.

Divide both sides of the equation by -2 to isolate x:

(-2x) / -2 = 72 / -2.

This simplifies to:

x = -36.

Therefore, the solution to the equation (1/6)x - 3 = (1/2)(x + 18) is x = -36.