What is -7<= 4x+27<33 ?

The solution to -7<= 4x+27<33 is -17/2 <= x< 3/2

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-7<= 4x+27<33

- 7 \leq 4 x + 27 < 33

- \frac{17}{2} \leq x < \frac{3}{2}

Interval Notation

[- \frac{17}{2}, \frac{3}{2})

Decimal Notation

- 8.5 \leq x < 1.5

Solution steps

- 7 \leq 4 x + 27 < 33

a \leq u < b

then

a \leq u and u < b

- 7 \leq 4 x + 27 and 4 x + 27 < 33

- 7 \leq 4 x + 27 : x \geq - \frac{17}{2}

4 x + 27 < 33 : x < \frac{3}{2}

Combine the intervals

x \geq - \frac{17}{2} and x < \frac{3}{2}

Merge Overlapping Intervals

- \frac{17}{2} \leq x < \frac{3}{2}

4 n + 7 > 43

\frac{( 6 x + 9 ) ( 6 x - 4 )}{6}

\frac{144}{36}

\frac{8 - 5 i}{7 + 6 i}

∣ 5 - 2 x ∣ \geq 7