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Popular >

1-|1-x/3 |<=-1/3

Solution

1 - 1 - \frac{x}{3} \leq - \frac{1}{3}

Solution

x \leq - 1 or x \geq 7

+1

Interval Notation

(- \infty, - 1] \cup [7, \infty)

Solution steps

1 - 1 - \frac{x}{3} \leq - \frac{1}{3}

Move

1

to the right side

- 1 - \frac{x}{3} \leq - \frac{4}{3}

Multiply both sides by

- 1

1 - \frac{x}{3} \geq \frac{4}{3}

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

1 - \frac{x}{3} \leq - \frac{4}{3} or 1 - \frac{x}{3} \geq \frac{4}{3}

1 - \frac{x}{3} \leq - \frac{4}{3} or 1 - \frac{x}{3} \geq \frac{4}{3}

x \leq - 1 or x \geq 7

Popular Examples

10^{-7.52}=(x^2)/(10^{-3)}

1 0^{- 7.52} = \frac{x ^{2}}{1 0 ^{- 3}}

simplify (x^2-y^2)/(x+y)simplify

\frac{x ^{2} - y ^{2}}{x + y}

7 v^{2} + 1 = 29

factor a(b-c)+d(c-b)factor

a (b - c) + d (c - b)

simplify (8+3i)^2 simplify

(8 + 3 i)^{2}

Frequently Asked Questions (FAQ)

What is 1-|1-x/3 |<=-1/3 ?
The solution to 1-|1-x/3 |<=-1/3 is x<=-1\lor x>= 7