Question

Решите неравенство 3x+7/8 - 2x+1/3 ≥ 1+x/2

Answer 1

$\frac{3x+7}{8} - \frac{2x+1}{3}\geq \frac{1+x}{2}\\\\\\ \frac{3(3x+7)}{8*3} - \frac{8(2x+1)}{3*8}\geq \frac{12(1+x)}{2*12}\\\\\\\\\frac{3*3x+3*7}{24} - \frac{8*2x+8*1}{24}\geq \frac{12*1+12*x}{2*12}\\\\\\\frac{9x+21-(16x+8)}{24} \geq\frac{12+12x}{2*12}$

9x+21-(16x+8)≥12+12x

9x+21-16x-8≥12+12x

-7x+13≥12+12x

13-12-7x≥12x

1-7x≥12

1≥7x+12x

1≥19x

1/19≥x

x ∈(-∞;1/19]

Ответ:x ∈(-∞;1/19]