Question

solve the inequality and graph the solution.
2 - 4k > 10
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( k \), we subtract 2 from both sides of the inequality \( 2 - 4k > 10 \). This gives us \( 2 - 4k - 2 > 10 - 2 \), which simplifies to \( -4k > 8 \).

Step2: Divide by -4 (and reverse inequality)

When we divide both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -4k > 8 \) by -4 gives \( \frac{-4k}{-4} < \frac{8}{-4} \), which simplifies to \( k < -2 \).

Answer:

The solution to the inequality \( 2 - 4k > 10 \) is \( k < -2 \). To graph this, we place an open circle at \( -2 \) (since the inequality is strict, \( k
eq -2 \)) and draw a ray to the left of \( -2 \) on the number line.