Question

Solve the inequality: \(-8x + 14 \geq 60\) OR \(-4x + 50 - 2x > -2x\), where "x" is a real number.

A. \(x \leq -\frac{23}{4}\)
B. \(x \leq -4\)
C. \(x > -2\)
D. There are no solutions
E. All values of "x" are solutions

Answer 1

To solve the compound inequality, we solve each inequality separately. The solution to the first inequality shows that x must be less than or equal to -23/4. The second inequality always holds true and does not restrict x, so the answer is A. x ≤ -rac{23}{4}.

Step-by-step explanation:

To solve the inequality, we will first look at each part of the compound inequality separately.

Solution for the first inequality:

-8x + 14 ≥ 60

Subtract 14 from both sides:

-8x ≥ 46

Divide both sides by -8 (remember to flip the inequality sign because we are dividing by a negative number):

x ≤ -rac{46}{8}

Simplify the fraction:

x ≤ -rac{23}{4} or x ≤ -5.75

Solution for the second inequality:

-4x + 50 - 2x > -2x

Combine like terms:

-6x + 50 > 0

Subtract 50 from both sides:

-6x > -50

Divide both sides by -6:

x < rac{50}{6}

However, this second inequality simplifies to a vacuous truth (always true), since -4x + 50 - 2x will always be greater than -2x alone. Thus, it doesn't impose any restrictions on the value of x.

Therefore, based on the first inequality, the correct answer is A. x ≤ -rac{23}{4}.