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Solve for x.
-8x+44 >= 60quad" AND "quad-4x+50 < 58
Choose 1 answer:
(A) x > -2
(B) x <= -2
(C) x=-2
(D) There are no solutions
(E) All values of x are solutions

Solve for x x .\newline -8 x+44 \geq 60 \quad \text { AND } \quad-4 x+50<58 \newlineChoose 11 answer:\newline(A) x>-2 \newline(B) x2 x \leq-2 \newline(C) x=2 x=-2 \newline(D) There are no solutions\newline(E) All values of x x are solutions

Full solution

Q. Solve for x x .\newline8x+4460 AND 4x+50<58 -8 x+44 \geq 60 \quad \text { AND } \quad-4 x+50<58 \newlineChoose 11 answer:\newline(A) x>2 x>-2 \newline(B) x2 x \leq-2 \newline(C) x=2 x=-2 \newline(D) There are no solutions\newline(E) All values of x x are solutions
  1. Solve First Inequality: Solve the first inequality 8x+4460-8x + 44 \geq 60. To isolate xx, we need to subtract 4444 from both sides of the inequality. 8x+44446044-8x + 44 - 44 \geq 60 - 44 8x16-8x \geq 16 Now, we divide both sides by 8-8. Remember that dividing by a negative number reverses the inequality sign. 8x/816/8-8x / -8 \leq 16 / -8 x2x \leq -2
  2. Solve Second Inequality: Solve the second inequality -4x + 50 < 58. Similarly, we subtract 5050 from both sides to isolate the 4x-4x term. -4x + 50 - 50 < 58 - 50 -4x < 8 Now, we divide both sides by 4-4, again remembering to reverse the inequality sign. -4x / -4 > 8 / -4 x > -2
  3. Combine Solutions: Combine the solutions from Step 11 and Step 22.\newlineWe have x2x \leq -2 from the first inequality and x > -2 from the second inequality.\newlineThese two inequalities contradict each other, as there is no number that is both greater than and less than or equal to 2-2 at the same time.\newlineTherefore, there are no solutions that satisfy both inequalities simultaneously.

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