Solve ((x-3)(x-2))/([(x^3)(x^2)]) (-(x-1))/x ≥0 - ScanMath

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Type your math problem... ((x-3)(x-2))/([(x^3)(x^2)]) (-(x-1))/x ≥0

Question

Solve the inequality

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3]

Evaluate

\frac{( x - 3 ) ( x - 2 )}{( x ^{3} \times x ^{2} )} \times \frac{- ( x - 1 )}{x} \geq 0

Find the domain

More Steps

\frac{( x - 3 ) ( x - 2 )}{( x ^{3} \times x ^{2} )} \times \frac{- ( x - 1 )}{x} \geq 0, x \neq = 0

Remove the parentheses

\frac{( x - 3 ) ( x - 2 )}{x ^{3} \times x ^{2}} \times \frac{- ( x - 1 )}{x} \geq 0

Simplify

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\frac{( x - 3 ) ( x - 2 ) ( - x + 1 )}{x ^{6}} \geq 0

Separate the inequality into 2 possible cases

{(x - 3) (x - 2) (- x + 1) \geq 0 x^{6} > 0 {(x - 3) (x - 2) (- x + 1) \leq 0 x^{6} < 0

Solve the inequality

More Steps

Evaluate

(x - 3) (x - 2) (- x + 1) \geq 0

Separate the inequality into 2 possible cases

{x - 3 \geq 0 (x - 2) (- x + 1) \geq 0 {x - 3 \leq 0 (x - 2) (- x + 1) \leq 0

Solve the inequality

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{x \geq 3 (x - 2) (- x + 1) \geq 0 {x - 3 \leq 0 (x - 2) (- x + 1) \leq 0

Solve the inequality

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{x \geq 3 1 \leq x \leq 2 {x - 3 \leq 0 (x - 2) (- x + 1) \leq 0

Solve the inequality

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{x \geq 3 1 \leq x \leq 2 {x \leq 3 (x - 2) (- x + 1) \leq 0

Solve the inequality

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{x \geq 3 1 \leq x \leq 2 {x \leq 3 x \in (- \infty, 1] \cup [2, + \infty)

Find the intersection

x \in \emptyset {x \leq 3 x \in (- \infty, 1] \cup [2, + \infty)

Find the intersection

x \in \emptyset x \in (- \infty, 1] \cup [2, 3]

Find the union

x \in (- \infty, 1] \cup [2, 3]

{x \in (- \infty, 1] \cup [2, 3] x^{6} > 0 {(x - 3) (x - 2) (- x + 1) \leq 0 x^{6} < 0

Solve the inequality

More Steps

{x \in (- \infty, 1] \cup [2, 3] x \neq = 0 {(x - 3) (x - 2) (- x + 1) \leq 0 x^{6} < 0

Solve the inequality

More Steps

Evaluate

(x - 3) (x - 2) (- x + 1) \leq 0

Separate the inequality into 2 possible cases

{x - 3 \geq 0 (x - 2) (- x + 1) \leq 0 {x - 3 \leq 0 (x - 2) (- x + 1) \geq 0

Solve the inequality

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{x \geq 3 (x - 2) (- x + 1) \leq 0 {x - 3 \leq 0 (x - 2) (- x + 1) \geq 0

Solve the inequality

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{x \geq 3 x \in (- \infty, 1] \cup [2, + \infty) {x - 3 \leq 0 (x - 2) (- x + 1) \geq 0

Solve the inequality

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{x \geq 3 x \in (- \infty, 1] \cup [2, + \infty) {x \leq 3 (x - 2) (- x + 1) \geq 0

Solve the inequality

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{x \geq 3 x \in (- \infty, 1] \cup [2, + \infty) {x \leq 3 1 \leq x \leq 2

Find the intersection

x \geq 3 {x \leq 3 1 \leq x \leq 2

Find the intersection

x \geq 3 1 \leq x \leq 2

Find the union

x \in [1, 2] \cup [3, + \infty)

{x \in (- \infty, 1] \cup [2, 3] x \neq = 0 {x \in [1, 2] \cup [3, + \infty) x^{6} < 0

Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is false for any value of x

{x \in (- \infty, 1] \cup [2, 3] x \neq = 0 {x \in [1, 2] \cup [3, + \infty) x \in / R

Find the intersection

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3] {x \in [1, 2] \cup [3, + \infty) x \in / R

Find the intersection

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3] x \in / R

Find the union

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3]

Check if the solution is in the defined range

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3], x \neq = 0

Solution

x \in (- \infty, 0) \cup (0, 1] \cup [2, 3]

Show Solution