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19 x+1 >= 3x
Which of the following best describes the solutions to the inequality shown?
Choose 1 answer:
(A)
x >= (1)/(16)
(B)
x >= -(1)/(22)
(C)
x <= -(1)/(16)
(D)
x >= -(1)/(16)

$19 x+1 \geq 3 x$ $\newline$ Which of the following best describes the solutions to the inequality shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x \geq \frac{1}{16}$ $\newline$ (B) $x \geq-\frac{1}{22}$ $\newline$ (C) $x \leq-\frac{1}{16}$ $\newline$ (D) $x \geq-\frac{1}{16}$

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Solve quadratic inequalities

Full solution

Q.

19 x+1 \geq 3 x

\newline

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

\newline

Choose

1

answer:

\newline

(A)

x \geq \frac{1}{16}

\newline

(B)

x \geq-\frac{1}{22}

\newline

(C)

x \leq-\frac{1}{16}

\newline

(D)

x \geq-\frac{1}{16}

Subtract $3x$ : To solve the inequality $19x + 1 \geq 3x$ , we need to isolate $x$ on one side. We can start by subtracting $3x$ from both sides of the inequality. $\newline$ Calculation: $19x + 1 - 3x \geq 3x - 3x$ $\newline$ Simplification: $16x + 1 \geq 0$
Subtract $1$ : Next, we subtract $1$ from both sides to further isolate the $x$ term. $\newline$ Calculation: $16x + 1 - 1 \geq 0 - 1$ $\newline$ Simplification: $16x \geq -1$
Divide by $16$ : Now, we divide both sides by $16$ to solve for $x$ . $\newline$ Calculation: $\frac{16x}{16} \geq \frac{-1}{16}$ $\newline$ Simplification: $x \geq -\frac{1}{16}$
Final Solution: We have found the solution to the inequality. The solution is $x \geq -\frac{1}{16}$ , which corresponds to one of the answer choices provided.

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