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State all integer values of
x in the interval
[4,9] that satisfy the following inequality:

-2x+8 <= -3
Answer:
x=

State all integer values of $x$ in the interval $[4,9]$ that satisfy the following inequality: $\newline$ $-2 x+8 \leq-3$ $\newline$ Answer: $x=$

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Solve quadratic inequalities

Full solution

Q. State all integer values of

x

in the interval

[4,9]

that satisfy the following inequality:

\newline

-2 x+8 \leq-3

\newline

Answer:

x=

Isolate x term: Solve the inequality $-2x + 8 \leq -3$ . $\newline$ Subtract $8$ from both sides to isolate the term with x. $\newline$ $-2x + 8 - 8 \leq -3 - 8$ $\newline$ $-2x \leq -11$
Divide by $-2$ : Divide both sides by $-2$ to solve for $x$ . Remember to reverse the inequality sign when dividing by a negative number. $\newline$ $-2x / -2 \geq -11 / -2$ $\newline$ $x \geq 11/2$ $\newline$ $x \geq 5.5$
Find integer solutions: Since we are looking for integer values of $x$ , we need to consider integers greater than or equal to $5.5$ within the interval $[4,9]$ . $\newline$ The integers that satisfy this condition are $6$ , $7$ , $8$ , and $9$ .

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