What is -1<= (x+1)/3 <= 1 ?

The solution to -1<= (x+1)/3 <= 1 is -4<= x<= 2

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-1<= (x+1)/3 <= 1

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

- 4 \leq x \leq 2

Interval Notation

[- 4, 2]

Solution steps

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

a \leq u \leq b

then

a \leq u and u \leq b

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

- 1 \leq \frac{x + 1}{3} : x \geq - 4

\frac{x + 1}{3} \leq 1 : x \leq 2

Combine the intervals

x \geq - 4 and x \leq 2

Merge Overlapping Intervals

- 4 \leq x \leq 2

(3 + 1)^{2}

- 1 = \frac{- 4 + k}{9}

(x - 5) (x + 9)^{2} - (x - 5)^{2} (x + 9)

3 x^{2} - \frac{1}{2} x - 188 = 0

b^{2} + 2 b - 15 = 0