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If $x \neq 0$ , which of the following values of $x$ satisfies the inequality $x+4x \leq 5$ ? $\newline$ I- $x>2$ $\newline$ II- $1 \leq x \leq 4$ $\newline$ III- $x<0$ $\newline$ A Only I $\newline$ B Only II $\newline$ C Both I and III $\newline$ D Both II and III

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Solutions to inequalities

Full solution

Q. If

x \neq 0

, which of the following values of

x

satisfies the inequality

x+4x \leq 5

?

\newline

I-

x>2

\newline

II-

1 \leq x \leq 4

\newline

III-

x<0

\newline

A Only I

\newline

B Only II

\newline

C Both I and III

\newline

D Both II and III

Combine Terms: Combine like terms in the inequality $x + 4x \leq 5$ . $5x \leq 5$
Divide and Isolate: Divide both sides of the inequality by $5$ to isolate $x$ . $\newline$ $x \leq 1$
Analyze Options I: Analyze each option: $\newline$ I- $x > 2$ : Check if any $x > 2$ satisfies $x \leq 1$ . $\newline$ No values greater than $2$ can be less than or equal to $1$ .
Analyze Options II: II- $1 \leq x \leq 4$ : Check if values between $1$ and $4$ satisfy $x \leq 1$ . $\newline$ Only $x = 1$ is possible, other values ( $2$ , $3$ , $4$ ) do not satisfy $x \leq 1$ .
Analyze Options III: III- $x < 0$ : Check if any $x < 0$ satisfies $x \leq 1$ . $\newline$ All negative values are less than $1$ , so they satisfy $x \leq 1$ .

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