Question

Which of the following are solutions to the inequality -7x+14>-3x-6? Select all that apply.

A.-10
B.10
C.-5
D.5
E.-3
F.3
G.0

Answer 1

To solve the inequality \(-7x + 14 > -3x - 6\), we can start by rearranging it.

1. Add \(7x\) to both sides:
\[
14 > 4x - 6
\]

2. Next, add \(6\) to both sides:
\[
20 > 4x
\]

3. Now, divide both sides by \(4\):
\[
5 > x
\]
or equivalently,
\[
x < 5
\]

This means that any \(x\) that is less than \(5\) is a solution to the inequality.

Now we can evaluate the given options:

A. \(-10 < 5\) (solution)
B. \(10 > 5\) (not a solution)
C. \(-5 < 5\) (solution)
D. \(5 \not< 5\) (not a solution)
E. \(-3 < 5\) (solution)
F. \(3 < 5\) (solution)
G. \(0 < 5\) (solution)

The solutions to the inequality are:

A. \(-10\)
C. \(-5\)
E. \(-3\)
F. \(3\)
G. \(0\)

Thus, the correct answers are A, C, E, F, and G.