An x-intercept means where does the equation when graphed cross the x-axis? Looking at the equation one can see that when graphed it gives a line in 3-d space. Whenever a line crosses the x-axis, it means that the y & z values must equal 0. Therefore, we must solve for x when y & z both have values of 0. We get:
-12x -y + 7z = 96 original equation
-12x - 0 + 7(0) = 96 substitute y & z with 0
-12x = 96 simplify
x = 96/-12 divide both sides by -12
x = -8 solve for x
The answer is the point (-8,0,0).
