Question

решите неравенства пожалуйста ​

Answer 1

( 1 )

$\displaystyle\\\frac{7x+2}{6} -x\leq \frac{5x+4}{3} -4x |*6\\\\\frac{6(7x+2)}{6} -x*6\leq \frac{6(5x+4)}{3} -4x*6\\\\\frac{7x+2}{1}-6x\leq \frac{2(5x+4)}{1}-24x\\ \\ 7x+2-6x\leq 2(5x+4)-24x\\\\7x+2-6x\leq 10x+8-24x\\\\7x-6x-10x+24x\leq8-2\\\\15x\leq 6\\\\x\leq 6:15\\\\x\leq 0,4$

x ∈ ( -∞ ; 0,4 ]

( 2 )

$\displaystyle\\\frac{4x+1}{3} -x>\frac{x+1}{2} -\frac{x-3}{4} |*12\\\\\frac{12(4x+1)}{3} -x*12>\frac{12(x+1)}{2} -\frac{12(x-3)}{4}\\ \\\frac{4(4x+1)}{1} -12x>\frac{6(x+1)}{1} -\frac{3(x-3)}{1}\\ \\4(4x+1)-12x>6(x+1)-3(x-3)\\\\16x+4-12x>6x+6-3x+9\\\\16x-12x-6x+3x>6+9-4\\\\x>11$

x ∈ ( 11 ; +∞ )

( 4 )

$\displaystyle\\\frac{5x-3}{4} -\frac{11x}{6} \geq \frac{2(1-x)}{3} +\frac{3x}{2}|*12\\ \\\frac{12(5x-3)}{4} -\frac{11x*12}{6} \leq \frac{12*2(1-x)}{3} +\frac{3x*12}{2}\\ \\\frac{3(5x-3)}{1} -\frac{11x*2}{1} \geq \frac{4*2(1-x)}{1} +\frac{3x*6}{1}\\ \\3(5x-3)-11x*2\geq 4*2(1-x)+3x*6\\\\15x-9-22x\geq 8(1-x)+18x\\\\15x-9-22x\geq 8-8x+18x\\\\15x-22x+8x-18x\geq 8+9\\\\-17x\geq 17\\\\17x\leq -17\\\\x\leq -17:17\\\\x\leq -1$

x ∈ ( -∞ ; -1 ]