What is (x+8)/(3x-2)>= 1 ?

The solution to (x+8)/(3x-2)>= 1 is 2/3 <x<= 5

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(x+8)/(3x-2)>= 1

\frac{x + 8}{3 x - 2} \geq 1

\frac{2}{3} < x \leq 5

Interval Notation

(\frac{2}{3}, 5]

Decimal Notation

0.66666 \dots < x \leq 5

Solution steps

\frac{x + 8}{3 x - 2} \geq 1

Rewrite in standard form

\frac{- 2 x + 10}{3 x - 2} \geq 0

Factor

\frac{- 2 x + 10}{3 x - 2} : \frac{- 2 ( x - 5 )}{3 x - 2}

\frac{- 2 ( x - 5 )}{3 x - 2} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x - 5 ) ) ( - 1 )}{3 x - 2} \leq 0 \cdot (- 1)

Simplify

\frac{2 ( x - 5 )}{3 x - 2} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x - 5 )}{3 x - 2}}{2} \leq \frac{0}{2}

Simplify

\frac{x - 5}{3 x - 2} \leq 0

Identify the intervals

\frac{2}{3} < x \leq 5

1 - \frac{8}{9}

(x - 2)^{2} + 3 = 0

1 - \frac{2}{3}

lo g_{3} (3^{4})

4 a^{3} b^{2} \cdot 3 a^{6} b^{5}