What is -4<= x^2+3x-4<= 6 ?

The solution to -4<= x^2+3x-4<= 6 is -5<= x<=-3\lor 0<= x<= 2

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-4<= x^2+3x-4<= 6

- 4 \leq x^{2} + 3 x - 4 \leq 6

- 5 \leq x \leq - 3 or 0 \leq x \leq 2

Interval Notation

[- 5, - 3] \cup [0, 2]

Solution steps

- 4 \leq x^{2} + 3 x - 4 \leq 6

a \leq u \leq b

then

a \leq u and u \leq b

- 4 \leq x^{2} + 3 x - 4 and x^{2} + 3 x - 4 \leq 6

- 4 \leq x^{2} + 3 x - 4 : x \leq - 3 or x \geq 0

x^{2} + 3 x - 4 \leq 6 : - 5 \leq x \leq 2

Combine the intervals

(x \leq - 3 or x \geq 0) and - 5 \leq x \leq 2

Merge Overlapping Intervals

- 5 \leq x \leq - 3 or 0 \leq x \leq 2

4.905 t^{2} - 23.64 t + 10 = 0

2 t^{2} - 20 t + 48 = 0

x^{2} - 6 x + 8 = x - 4

4 (6) + 7 (2) = - 19

What is -4<= x^2+3x-4<= 6 ?
The solution to -4<= x^2+3x-4<= 6 is -5<= x<=-3\lor 0<= x<= 2