Solve for x. (x - 2)(x - 3) ≤ 0 Write a compound inequality like 1 3. ______

Find Critical Points: Find the critical points of (x - 2)(x - 3). (x - 2)(x - 3) = 0 x - 2 = 0 implies x = 2. x - 3 = 0 implies x = 3. Critical points: 2, 3.Identify Intervals: Identify the intervals using the critical points. 2 and 3 divide the number line into three parts. Intervals: (-∞, 2), (2, 3), (3, ∞).Test Sign (-∞, 2): Test the sign of (x - 2)(x - 3) over (-∞, 2). Pick x = 1 (which is in the interval). Sign of (x - 2): -. Sign of (x - 3): -. Sign of (x - 2)(x - 3): (-)(-) = +.Test Sign (2, 3): Test the sign of (x - 2)(x - 3) over (2, 3). Pick x = 2.5 (which is in the interval). Sign of (x - 2): +. Sign of (x - 3): -. Sign of (x - 2)(x - 3): (+)(-) = -.Test Sign (3, ∞): Test the sign of (x - 2)(x - 3) over (3, ∞). Pick x = 4 (which is in the interval). Sign of (x - 2): +. Sign of (x - 3): +. Sign of (x - 2)(x - 3): (+)(+) = +.Compound Inequality: (x - 2)(x - 3) ≤ 0. Find the solution as a compound inequality. (x - 2)(x - 3) is non-positive over [2, 3]. Compound inequality: 2 ≤ x ≤ 3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $x$ . $\newline$ $(x - 2)(x - 3) \leq 0$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.______

View step-by-step help

Home

Math Problems

Algebra 2

Solve quadratic inequalities

Full solution

Q. Solve for

x

\newline

(x - 2)(x - 3) \leq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Critical Points: Find the critical points of $(x - 2)(x - 3)$ . $(x - 2)(x - 3) = 0$ $x - 2 = 0$ implies $x = 2$ . $x - 3 = 0$ implies $x = 3$ .Critical points: $2, 3$ .
Identify Intervals: Identify the intervals using the critical points. $\newline$ $2$ and $3$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 2$ ), $(2, 3)$ , $(3, \infty)$ .
Test Sign $(-\infty, 2)$ : Test the sign of $(x - 2)(x - 3)$ over $(-\infty, 2)$ . $\newline$ Pick $x = 1$ (which is in the interval). $\newline$ Sign of $(x - 2)$ : -. $\newline$ Sign of $(x - 3)$ : -. $\newline$ Sign of $(x - 2)(x - 3)$ : $(-)(-) = +$ .
Test Sign $(2, 3)$ : Test the sign of $(x - 2)(x - 3)$ over $(2, 3)$ . $\newline$ Pick $x = 2.5$ (which is in the interval). $\newline$ Sign of $(x - 2)$ : +. $\newline$ Sign of $(x - 3)$ : -. $\newline$ Sign of $(x - 2)(x - 3)$ : $(+)(-) = -$ .
Test Sign \(3, \infty): Test the sign of x - \(2)(x - $3$ ) over \(3, \infty). $\newline$ Pick x = \(4) (which is in the interval). $\newline$ Sign of x - \(2): +. $\newline$ Sign of x - \(3): +. $\newline$ Sign of x - \(2)(x - $3$ ): (+)(+) = +.
Compound Inequality: $(x - 2)(x - 3) \leq 0$ . Find the solution as a compound inequality. $(x - 2)(x - 3)$ is non-positive over $[2, 3]$ . Compound inequality: $2 \leq x \leq 3$ .