What is |1.25+0.75x|<= 3.75 ?

The solution to |1.25+0.75x|<= 3.75 is -20/3 <= x<= 10/3

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|1.25+0.75x|<= 3.75

∣ 1.25 + 0.75 x ∣ \leq 3.75

- \frac{20}{3} \leq x \leq \frac{10}{3}

Interval Notation

[- \frac{20}{3}, \frac{10}{3}]

Decimal Notation

- 6.66666 \dots \leq x \leq 3.33333 \dots

Solution steps

∣ 1.25 + 0.75 x ∣ \leq 3.75

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3.75 \leq 1.25 + 0.75 x \leq 3.75

1.25 + 0.75 x \geq - 3.75 and 1.25 + 0.75 x \leq 3.75

x \geq - \frac{20}{3} and x \leq \frac{10}{3}

Merge Overlapping Intervals

- \frac{20}{3} \leq x \leq \frac{10}{3}

∣ 2 - x ∣ < 2 x + 3

\frac{5}{2 5 ( 7 ) + 1}

x^{2} + 1 5^{2} = 1 7^{2}

- 15 x + 4 \leq 109

100 - 140 x + 49 x^{2}

What is |1.25+0.75x|<= 3.75 ?
The solution to |1.25+0.75x|<= 3.75 is -20/3 <= x<= 10/3