Question

What are the correct steps to solve this inequality, and which is the correct graph of the solution? (The green region is the shaded area.)%0D%0A%0D%0A−4x−46<−38%0D%0A−%0D%0A4%0D%0A𝑥%0D%0A−%0D%0A46%0D%0A<%0D%0A−%0D%0A38%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AAdd 46, divide by -4, flip the inequality sign, x>−2%0D%0A𝑥%0D%0A>%0D%0A−%0D%0A2%0D%0A %0D%0AAdd 46, divide by -4, flip the inequality sign, x is greater than negative 2 %0D%0A%0D%0AAdd 46, multiply by -4, flip the inequality sign, x>−2%0D%0A𝑥%0D%0A>%0D%0A−%0D%0A2%0D%0A %0D%0AAdd 46, multiply by -4, flip the inequality sign, x is greater than negative 2 %0D%0A%0D%0AAdd 46, divide by -4, x<−2%0D%0A𝑥%0D%0A<%0D%0A−%0D%0A2%0D%0A %0D%0AAdd 46, divide by -4, x<−2%0D%0A𝑥%0D%0A<%0D%0A−%0D%0A2%0D%0A %0D%0A%0D%0AAdd 46, divide by -4, flip the inequality sign, x>−2%0D%0A𝑥%0D%0A>%0D%0A−%0D%0A2%0D%0A

Answer 1

To solve the inequality \(-4x - 46 < -38\), follow these steps:

1. Add 46 to both sides:
   \(-4x - 46 + 46 < -38 + 46\)
   This simplifies to:
   \(-4x < 8\)

2. Divide by -4:
   \(-4x / -4 > 8 / -4\)
   (Remember to flip the inequality sign when dividing by a negative number.)
   This simplifies to:
   \(x > -2\)

Thus, the correct solution for the inequality is \(x > -2\).

Conclusion

Now, about the responses you provided, the correct options would be:

• Add 46, divide by -4, flip the inequality sign, \(x > -2\).

Regarding the graph of the solution:

• The graph would depict an open circle at \(-2\) with a shaded region extending to the right, indicating that all values greater than \(-2\) are part of the solution. The green region mentioned in your question likely represents that area.