Question

Solve the inequality - 1 >-2(x - 4) - 5(4x - 7).

A) x< 2
B) x< 2
C) x>23
D) x> 8

Answer 1

To solve the inequality -1 > -2(x - 4) - 5(4x - 7), distribute the negatives, combine like terms, and then isolate the variable. After simplifying, the solution is x > 2, assuming there is a typo in the provided options.

Step-by-step explanation:

To solve the inequality -1 > -2(x - 4) - 5(4x - 7), we first distribute the negative numbers across the parentheses:

-1 > -2x + 8 - 20x + 35

Then, we combine like terms:

-1 > -22x + 43

Next, we isolate the variable term by moving constants to the other side:

-1 - 43 > -22x

-44 > -22x

Now, divide both sides by -22, and remember to reverse the inequality sign when dividing by a negative number:

2 < x

So, the solution to the inequality is x > 2, which corresponds to choice B) x < 2, assuming there is a typo in the options and they meant to say B) x > 2.