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Which of the following numbers is NOT a solution $\newline$ of the inequality $3x - 5 \geq 4 - 3x$ ? $\newline$ A) $-1$ $\newline$ B) $-2$ $\newline$ C) $-3$ $\newline$ D) $-5$

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Solutions to inequalities

Full solution

Q. Which of the following numbers is NOT a solution

\newline

of the inequality

3x - 5 \geq 4 - 3x

?

\newline

A)

-1

\newline

B)

-2

\newline

C)

-3

\newline

D)

-5

Simplify inequality: Simplify the inequality by adding $3x$ to both sides: $\newline$ $3x - 5 + 3x \geq 4 - 3x + 3x$ $\newline$ $6x - 5 \geq 4$
Add to isolate $x$ : Add $5$ to both sides to isolate the term with $x$ : $6x - 5 + 5 \geq 4 + 5$ $6x \geq 9$
Divide to solve $x$ : Divide both sides by $6$ to solve for $x$ : $\frac{6x}{6} \geq \frac{9}{6}$ $x \geq 1.5$
Check solutions: Check each option to see if it satisfies $x \geq 1.5$ : $\newline$ A) $x = -1$ : $-1 \geq 1.5$ (False) $\newline$ B) $x = -2$ : $-2 \geq 1.5$ (False) $\newline$ C) $x = -3$ : $-3 \geq 1.5$ (False) $\newline$ D) $x = -5$ : $-5 \geq 1.5$ (False)

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