Find the value of x for which the equation below is true.

|5x - 2y| |18|
|x + 6y|=|10|

A.16
B.-1
C.4
D.1

To find the value of x for which the equation is true, we can use the property of absolute values. The property states that for any real number a, |a| = a if a ≥ 0, and |a| = -a if a < 0.

Let's analyze the given equations:

Equation 1: |5x - 2y| = 18
Equation 2: |x + 6y| = 10

For equation 1, if (5x - 2y) ≥ 0, we can rewrite the equation as:
5x - 2y = 18

If (5x - 2y) < 0, we can rewrite the equation as:
-(5x - 2y) = 18
-5x + 2y = 18

Now let's focus on equation 2, if (x + 6y) ≥ 0, we can rewrite the equation as:
x + 6y = 10

If (x + 6y) < 0, we can rewrite the equation as:
-(x + 6y) = 10
-x - 6y = 10

We now have the following systems of equations:

System 1:
5x - 2y = 18
x + 6y = 10

System 2:
-5x + 2y = 18
x + 6y = 10

To solve these systems of equations, we can use the method of substitution or elimination.

Let's solve System 1 using the method of substitution:

From the equation x + 6y = 10, we can rewrite it as x = 10 - 6y.

Substituting x = 10 - 6y into the first equation of System 1:
5(10 - 6y) - 2y = 18
50 - 30y - 2y = 18
-32y = -32
y = 1

Now substitute y = 1 back into the equation x + 6y = 10:
x + 6(1) = 10
x + 6 = 10
x = 4

Therefore, the solution for System 1 is x = 4 and y = 1.

Now let's solve System 2 using the method of elimination:

Multiply both sides of the equation x + 6y = 10 by 5 to eliminate x:
5(x + 6y) = 5(10)
5x + 30y = 50

Adding the equations -5x + 2y = 18 and 5x + 30y = 50 eliminates the x-term:
-5x + 2y + 5x + 30y = 18 + 50
32y = 68
y = 2.125

Substitute y = 2.125 back into the equation x + 6y = 10:
x + 6(2.125) = 10
x + 12.75 = 10
x = -2.75

Therefore, the solution for System 2 is x = -2.75 and y = 2.125.

Comparing the solutions of both systems, we find that x = 4 does not satisfy the second equation (|x + 6y| = 10), but x = -2.75 does satisfy both equations.

So, the value of x for which the equation |5x - 2y| = 18 and |x + 6y| = 10 is true is x = -2.75.

However, none of the given answer choices match x = -2.75. Therefore, none of the answer choices A, B, C, or D is correct.