Student's error is –5 < x.
Solution:
Step 1: Given inequality
31 < –5x + 6
Step 2: Subtract 6 from both sides of the inequality.
31 – 6 < –5x + 6 – 6
25 < –5x
Step 3: Multiply both sides by –1 to reverse the inequality.
25 × (–1) > –5x × (–1)
–25 > 5x
Step 4: Divide by 5 on both sides.
–5 > x
The correct answer is –5 > x.
Student's error is –5 < x.
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The desired plane will have a direction vector that is perpendicular to that of the given line (4, -3, 1) and that of the given plane (2, 5, 4). Computing the cross product of these gives (-17, -14, 26).
Since the plane contains the point (-4, -3, -1), we can find the constant (d) in ax+by+cz=d using the dot-product of the point and the direction vector just found.
-17·(-4) -14·(-3) +26·(-1) = 68 +42 -26 = 84
Your plane can be written as
-17x -14y +26z = 84
Solving for z, you get
z = (17x +14y +84)/26
or, if you prefer, ...
z = (17/26)x +(7/13)y +42/13