What is |4x+7|>= x+5 ?

The solution to |4x+7|>= x+5 is x =-2/3

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|4x+7|>= x+5

∣ 4 x + 7 ∣ \geq x + 5

x \leq - \frac{12}{5} or x \geq - \frac{2}{3}

Interval Notation

(- \infty, - \frac{12}{5}] \cup [- \frac{2}{3}, \infty)

Decimal

x \leq - 2.4 or x \geq - 0.66666 \dots

Solution steps

∣ 4 x + 7 ∣ \geq x + 5

Find positive and negative intervals

x < - \frac{7}{4}, x \geq - \frac{7}{4}

Solve the inequality for each interval

x \leq - \frac{12}{5} or x \geq - \frac{2}{3}

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

(- \frac{8}{17})^{2} - (- \frac{15}{17})^{2}

\frac{a y - a x + b y - b x}{2 a y - b y - 2 a x + b x}

- 5 x + 1 < 21

x^{2} - 5 x - 20 = 0