Solve the inequality and graph the solution.
3k>5k+12
show your work
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+ ∞
To solve the inequality 3k > 5k + 12, you need to isolate the variable k. Here's how you can do it step by step:
1. Start by subtracting 5k from both sides of the inequality to get the variables on one side:
3k - 5k > 5k + 12 - 5k
Simplifying this expression, we get:
-2k > 12
2. Next, divide both sides of the inequality by -2. Since we are dividing by a negative number, it reverses the inequality:
-2k / -2 < 12 / -2
Simplifying further, we have:
k < -6
So the value of k is less than -6 to satisfy the given inequality.
Now let's graph the solution on a number line:
-∞ -6 +∞
------------------●-------------------
Solution: k < -6
The open dot at -6 indicates that -6 is not included in the solution since the inequality is strict. The shaded part extending to the left of -6 represents all values of k that make the inequality 3k > 5k + 12 true.
To solve the inequality 3k > 5k + 12, let's start by isolating the variable k on one side of the inequality.
Step 1: Subtract 5k from both sides to get rid of the 5k on the right side:
3k - 5k > 5k - 5k + 12
Simplifying, we have:
-2k > 12
Step 2: Divide both sides of the inequality by -2. Since we are multiplying/dividing by a negative number, the direction of the inequality sign will flip:
-2k / -2 < 12 / -2
Simplifying further:
k < -6
So, the solution to the inequality is k < -6.
To graph the solution, we can represent the solution on a number line. Draw a line and mark a point at -6, which represents the boundary of the inequality. Since the inequality is strict (k < -6), we will use an open circle at -6 to exclude -6 from the solution.
Next, shade the region to the left of -6 since we are looking for all values of k less than -6. Since the inequality is not inclusive of -6, we do not darken the -6 on the number line.
The graph should show an open circle at -6 and a shaded region to the left of -6.