Question

ajutatima,multumesc! clik pe poza

Answer 1

         
$3a) \\ 4x-16\ \textless \ 0 \\ 4x\ \textless \ 16 \\ x\ \textless \ \frac{16}{4} \\ x\ \textless \ 4 \\ \\ 3b) \\ -2x+6 \leq 0 \\ -2x \leq -6 \;\;\;|*(-1) \\ 2x \geq 6 \\ x \geq \frac{6}{2} \\ x \geq 3$

$3c) \\ 6x+12\ \textgreater \ 3x \\ 6x-3x\ \textgreater \ -12 \\ 3x\ \textgreater \ -12 \\ x\ \textgreater \ \frac{-12}{3} \\ x\ \textgreater \ -4 \\ \\ 3d) \\ 0,4x+2 \geq 0,8 \\ 0,4x \geq 0,8-2 \\ 0,4x \geq -1,2 \\ x \geq \frac{-1,2}{0,4} \\ x \geq -3$

$3e) \\ \sqrt{2} x- \sqrt{72} \ \textgreater \ x \sqrt{8} \\ x\sqrt{2}-x \sqrt{8} \ \textgreater \ \sqrt{72} \\ x\sqrt{2}-2x \sqrt{2} \ \textgreater \ 6\sqrt{2} \\ x\sqrt{2}(1-2)\ \textgreater \ 6\sqrt{2} \\ -x\sqrt{2}\ \textgreater \ 6\sqrt{2}\;\;\;|*(-1) \\ x\sqrt{2}\ \textgreater \ -6\sqrt{2} \\ x\ \textgreater \ \frac{-6\sqrt{2}}{\sqrt{2}} \\ x\ \textgreater \ -6$

$3f) \\ 3,7x-18 \geq 19 \\ 3,7x \geq 19 +18 \\ 3,7x \geq 37 \\ x \geq \frac{37}{3,7} \\ x \geq 10 \\ \\ 3g) \\ \frac{2}{3} x- \frac{1}{4} \geq \frac{5}{6} \\ \\ \frac{4*2}{12} x- \frac{3*1}{12} \geq \frac{2*5}{12}\;\;\;|*12 \\ 8x-3 \geq 10 \\ 8x \geq 10+3 \\ 8x \geq 13 \\ x \geq \frac{13}{8}$

$3h) \\ \frac{x+1}{3} \ \textless \ \frac{2x+1}{4} \\ \\ \frac{4(x+1)}{12} \ \textless \ \frac{3(2x+1)}{12} \;\;\; |*12 \\ 4x+4\ \textless \ 6x+3 \\ 4x-6x\ \textless \ 3-4 \\ -2x\ \textless \ -1\;\;\; |*(-1) \\ 2x\ \textgreater \ 1 \\ x\ \textgreater \ \frac{1}{2}$

$3i) \\ \frac{x-3}{2}+ \frac{x}{3} \ \textless \ \frac{3x-5}{4} \\ \\ \frac{6(x-3)}{12}+ \frac{4x}{12} \ \textless \ \frac{3(3x-5)}{12} \;\;\;|*12 \\ 6x-18+4x\ \textless \ 9x-15 \\ 6x+4x-9x\ \textless \ -15+18 \\ x\ \textless \ 3$