What is |(12x-4)/2 |<= 10 ?

The solution to |(12x-4)/2 |<= 10 is -4/3 <= x<= 2

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|(12x-4)/2 |<= 10

\frac{12 x - 4}{2} \leq 10

- \frac{4}{3} \leq x \leq 2

Interval Notation

[- \frac{4}{3}, 2]

Decimal Notation

- 1.33333 \dots \leq x \leq 2

Solution steps

\frac{12 x - 4}{2} \leq 10

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 10 \leq \frac{12 x - 4}{2} \leq 10

\frac{12 x - 4}{2} \geq - 10 and \frac{12 x - 4}{2} \leq 10

x \geq - \frac{4}{3} and x \leq 2

Merge Overlapping Intervals

- \frac{4}{3} \leq x \leq 2

12 x^{2} - 48 x + 35 = 0

(6^{3})^{5}

x^{3} + 4 x^{2} - 9 x - 36

\frac{x}{2} - 1 = \frac{3 - x}{5}

7 b^{2} - 63 b + 140