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4-2x >= 1-x
Which of the following best describes the solutions to the inequality shown?
Choose 1 answer:
(A)
x <= 1
(B)
x >= 3
(C)
x <= 3
(D)
x <= -5

$4-2 x \geq 1-x$ $\newline$ Which of the following best describes the solutions to the inequality shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x \leq 1$ $\newline$ (B) $x \geq 3$ $\newline$ (C) $x \leq 3$ $\newline$ (D) $x \leq-5$

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Identify solutions to inequalities

Full solution

Q.

4-2 x \geq 1-x

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

Choose

1

answer:

\newline

(A)

x \leq 1

\newline

(B)

x \geq 3

\newline

(C)

x \leq 3

\newline

(D)

x \leq-5

Add $x$ to both sides: Simplify the inequality by adding $x$ to both sides: $4 - 2x + x \geq 1 - x + x$
Subtract $4$ from both sides: This simplifies to $4 - x \geq 1$ ; now subtract $4$ from both sides: $4 - 4 - x \geq 1 - 4$
Multiply by $-1$ and flip: This results in $-x \geq -3$ ; multiply both sides by $-1$ (and remember to flip the inequality sign): $-1(-x) \leq -1(-3)$
Final result: Simplified, this gives $x \leq 3$

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