What is -1<|((3x+4))/2 |<= 3 ?

The solution to -1<|((3x+4))/2 |<= 3 is -10/3 <= x<= 2/3

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-1<|((3x+4))/2 |<= 3

- 1 < \frac{( 3 x + 4 )}{2} \leq 3

- \frac{10}{3} \leq x \leq \frac{2}{3}

Interval Notation

[- \frac{10}{3}, \frac{2}{3}]

Decimal Notation

- 3.33333 \dots \leq x \leq 0.66666 \dots

Solution steps

- 1 < \frac{( 3 x + 4 )}{2} \leq 3

a < u \leq b

then

a < u and u \leq b

- 1 < \frac{( 3 x + 4 )}{2} and \frac{( 3 x + 4 )}{2} \leq 3

- 1 < \frac{3 x + 4}{2} :

True for all

x

\frac{3 x + 4}{2} \leq 3 : - \frac{10}{3} \leq x \leq \frac{2}{3}

Combine the intervals

True for all x and - \frac{10}{3} \leq x \leq \frac{2}{3}

Merge Overlapping Intervals

- \frac{10}{3} \leq x \leq \frac{2}{3}

1 < 3 x - 5 < 1

0 < \frac{5}{x} < \frac{8}{9}

- 1 < - 2 x + 5 < 1

1 \leq \frac{( 2 - x )}{( x + 1 )} \leq 2

0 < - \frac{x}{3} < 1

What is -1<|((3x+4))/2 |<= 3 ?
The solution to -1<|((3x+4))/2 |<= 3 is -10/3 <= x<= 2/3