Solve the inequality and graph the solution.

Question

3k>5k+12
show your work

Answer 1

To solve the inequality 3k > 5k + 12, we can subtract 5k from both sides of the inequality to isolate the variable:

3k - 5k > 5k + 12 - 5k

-2k > 12

Since we have a negative coefficient on the variable, we must multiply both sides by -1 and reverse the inequality sign:

(-2k)(-1) < 12(-1)

2k < -12

Now, we can divide both sides by 2 to solve for k:

(2k)/2 < -12/2

k < -6

Therefore, the solution to the inequality is k < -6.

To graph the solution, we can draw an open circle at -6 on a number line, and shade to the left of the circle to represent all values less than -6.

Graph:
o----------------
-∞ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6+ ∞