Question

[4x+2 > 10 { and } -3x-1 > 5]

a) (x > 2 { and } x < -2)
b) (x < 2 { and } x > -2)
c) (x > -2 { and } x < 2)
d) (x < -2 { and } x > 2)

Answer 1

The system of inequalities 4x+2 > 10 and -3x-1 > 5 has no solution as the inequality x > 2 and x < -2 cannot be true simultaneously. Therefore, none of the answer options provided is correct, as they each propose an impossible range of values for x.

Step-by-step explanation:

To solve the system of inequalities 4x+2 > 10 and -3x-1 > 5, we need to solve each inequality separately and then find the intersection of the solutions.

Firstly, let's solve the first inequality:

• 4x + 2 > 10
• 4x > 8 (Subtract 2 from both sides)
• x > 2 (Divide both sides by 4)

Now, let's solve the second inequality:

• -3x - 1 > 5
• -3x > 6 (Add 1 to both sides)
• x < -2 (Divide both sides by -3, remember to reverse the inequality sign since we are dividing by a negative number)

Combining these two results, we see that there is no value of x that can be both greater than 2 and less than -2 at the same time. Therefore, there is no solution to the system of inequalities. None of the provided answer choices are correct since they each suggest a range of x values that do not overlap.