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Popular >

-3|1-4q|-4<=-14

Solution

- 3 ∣ 1 - 4 q ∣ - 4 \leq - 14

Solution

q \leq - \frac{7}{12} or q \geq \frac{13}{12}

+2

Interval Notation

(- \infty, - \frac{7}{12}] \cup [\frac{13}{12}, \infty)

Decimal Notation

q \leq - 0.58333 \dots or q \geq 1.08333 \dots

Solution steps

- 3 ∣ 1 - 4 q ∣ - 4 \leq - 14

Move

4

to the right side

- 3 ∣ 1 - 4 q ∣ \leq - 10

Multiply both sides by

- 1

3 ∣ 1 - 4 q ∣ \geq 10

Divide both sides by

3

∣ 1 - 4 q ∣ \geq \frac{10}{3}

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

1 - 4 q \leq - \frac{10}{3} or 1 - 4 q \geq \frac{10}{3}

1 - 4 q \leq - \frac{10}{3} or 1 - 4 q \geq \frac{10}{3}

q \leq - \frac{7}{12} or q \geq \frac{13}{12}

Popular Examples

simplify-X^2*X simplify

- X^{2} \cdot X

64 x^{2} + 80 x + 25 = 0

simplify a/((b/c))simplify

\frac{a}{( \frac{b}{c} )}

simplify (3pi)/2 simplify

\frac{3 π}{2}

(x - 9)^{2} = 144

Frequently Asked Questions (FAQ)

What is -3|1-4q|-4<=-14 ?
The solution to -3|1-4q|-4<=-14 is q<=-7/12 \lor q>= 13/12