What is -3<= 3x+7<= 1/2 ?

The solution to -3<= 3x+7<= 1/2 is -10/3 <= x<=-13/6

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-3<= 3x+7<= 1/2

- 3 \leq 3 x + 7 \leq \frac{1}{2}

- \frac{10}{3} \leq x \leq - \frac{13}{6}

Interval Notation

[- \frac{10}{3}, - \frac{13}{6}]

Decimal Notation

- 3.33333 \dots \leq x \leq - 2.16666 \dots

Solution steps

- 3 \leq 3 x + 7 \leq \frac{1}{2}

a \leq u \leq b

then

a \leq u and u \leq b

- 3 \leq 3 x + 7 and 3 x + 7 \leq \frac{1}{2}

- 3 \leq 3 x + 7 : x \geq - \frac{10}{3}

3 x + 7 \leq \frac{1}{2} : x \leq - \frac{13}{6}

Combine the intervals

x \geq - \frac{10}{3} and x \leq - \frac{13}{6}

Merge Overlapping Intervals

- \frac{10}{3} \leq x \leq - \frac{13}{6}

- 2 x \geq - 4 (1 - 3 x)

3 x^{2} - 6 = 0

1 1^{- 2}

\frac{30 !}{5 ! ( 30 - 5 ) !}

0.15 = y - 0.45