Question

What is the solution to the equation 0.24 [x - 10.2 ] = 6 when solving for x?


11.64
14.8
35.2
16.44

Answer 1

To solve for x, we can start by multiplying both sides of the equation by the reciprocal of 0.24, which is 1/0.24 or 25/6. This gives us:

(25/6)(0.24[x-10.2]) = (25/6)(6)

The 0.24 and 6 on the left side cancel out, leaving us with:

25/6[x-10.2] = 25

Next, we can distribute the 25/6 to both terms inside the brackets:

(25/6)x - (25/6)(10.2) = 25

Simplifying the right side gives us:

(25/6)x - (25/6)(10.2) = 25/1

To find the solution for x, we can first multiply (25/6)(10.2) to get:

(25/6)(10.2) = 43.75

Substituting this value back into the equation, we have:

(25/6)x - 43.75 = 25/1

Next, we can move the constant term to the right side by adding 43.75 to both sides:

(25/6)x = 25/1 + 43.75

Simplifying the right side gives us:

(25/6)x = 68.75

Finally, we can solve for x by multiplying both sides of the equation by 6/25, which is the reciprocal of 25/6:

(6/25)(25/6)x = (6/25)(68.75)

The (25/6) and (6/25) on the left side cancel out, leaving us with:

x = 68.75(6/25)

Simplifying the right side gives us:

x = 16.44

Therefore, the solution to the equation 0.24[x - 10.2] = 6 is x = 16.44.