image imagewidth (px) 2 3.75k | material_type stringclasses 2
values | latex listlengths 1 1 |
|---|---|---|
HW | [
"(1) $\\displaystyle 0$ (2) $\\displaystyle 1$ (3) $\\displaystyle 1$"
] | |
HW | [
"$\\displaystyle 5 x+4 \\geq x+16$"
] | |
HW | [
"$\\displaystyle 5 x+4 \\geq x+16$"
] | |
HW | [
"$\\displaystyle 4 x \\geqslant 12 \\quad x<3$"
] | |
HW | [
"$\\displaystyle x \\geqslant 3$"
] | |
HW | [
"$\\displaystyle 5x+4 \\geq x+16 \\quad 8-5 x>5-4 x$"
] | |
HW | [
"$\\displaystyle 5x+4 \\geq x+16 \\quad 8-5 x>5-4 x$"
] | |
HW | [
"$\\displaystyle (k+5)(k-5)<0, \\; -5 < k < 5 $"
] | |
HW | [
"good"
] | |
HW | [
"good"
] | |
HW | [
"$\\displaystyle x^{3}+8 x^{2}+(k+16) x+4 k=0$"
] | |
HW | [
"$\\displaystyle (x+4)\\left(x^{2}+4 x+k\\right)=0$"
] | |
HW | [
"$\\displaystyle (x+4)\\left(x^{2}+4 x+k\\right)=0$"
] | |
HW | [
"$\\displaystyle x+4=0$ or $\\displaystyle x^{2}+4 x+k=0$"
] | |
HW | [
"$\\displaystyle x+4=0$ or $\\displaystyle x^{2}+4 x+k=0$"
] | |
HW | [
"$\\displaystyle 10x^{2}-k<0 \\Rightarrow x^{2}<\\frac{k}{10} \\Rightarrow -\\sqrt{\\frac{k}{10}} < x < \\sqrt{\\frac{k}{10}}$"
] | |
HW | [
"110"
] | |
HW | [
"$\\displaystyle 15 k^{2}+4 k-32>0$"
] | |
HW | [
"$\\displaystyle k<-\\frac{8}{5}, k>\\frac{4}{3}$"
] | |
HW | [
"$\\displaystyle |x-a| \\leq 6$"
] | |
HW | [
"$\\displaystyle |x-a| \\leq 6$"
] | |
HW | [
"$\\displaystyle -6 \\leq x-a \\leq 6,-6+a \\leq x \\leq 6+a,-6+a=-3, a=3$"
] | |
HW | [
"$\\displaystyle -6 \\leq x-a \\leq 6,-6+a \\leq x \\leq 6+a,-6+a=-3, a=3$"
] | |
HW | [
"good"
] | |
HW | [
"good"
] | |
HW | [
"27"
] | |
HW | [
"27"
] | |
HW | [
"$\\displaystyle \\therefore-2(m-4)<0, \\quad 4(m+4)>0$."
] | |
HW | [
"$\\displaystyle m>4 \\quad m>-4$"
] | |
HW | [
"$\\displaystyle m>4 \\quad m>-4$"
] | |
HW | [
"$\\displaystyle m>4$"
] | |
HW | [
"$\\displaystyle x^{2}=t \\quad(t>0)$"
] | |
HW | [
"$\\displaystyle x^{2}=t \\quad(t>0)$"
] | |
HW | [
"$\\displaystyle t^{2}+t-30=0$"
] | |
HW | [
"$\\displaystyle \\text{t}=-6$ or $\\displaystyle 5$ "
] | |
HW | [
"$\\displaystyle \\text{t}=-6$ or $\\displaystyle 5$ "
] | |
HW | [
"$\\displaystyle x^{2}=5$"
] | |
HW | [
"$\\displaystyle x=\\pm \\sqrt{5}$"
] | |
HW | [
"$\\displaystyle x^{2}-7 x+19<0$"
] | |
HW | [
"$\\displaystyle \\left(x+\\frac{1}{7}\\right)\\left(x-\\frac{7}{8}\\right)<0$"
] | |
HW | [
"$\\displaystyle x^{2}-\\frac{41}{56} x-\\frac{1}{8}<0$"
] | |
HW | [
"$\\displaystyle x^{2}-\\frac{41}{56} x-\\frac{1}{8}<0$"
] | |
HW | [
"$\\displaystyle a=1$"
] | |
HW | [
"$\\displaystyle a=1$"
] | |
HW | [
"$\\displaystyle b=-\\frac{41}{36}$"
] | |
HW | [
"$\\displaystyle \\therefore \\frac{15}{56}$"
] | |
HW | [
"$\\displaystyle \\therefore \\frac{15}{56}$"
] | |
HW | [
"$\\displaystyle 120x+101x>642.$"
] | |
HW | [
"$\\displaystyle 221 x>642 .$"
] | |
HW | [
"$\\displaystyle x>\\frac{642}{221}$"
] | |
HW | [
"$\\displaystyle x>\\frac{642}{221}$"
] | |
HW | [
"Good!"
] | |
HW | [
"$\\displaystyle -4 x-16) x^{2}$"
] | |
HW | [
"$\\displaystyle 2 y^{2}-8 y+16=36$"
] | |
HW | [
"$\\displaystyle y^{2}-4 y-10=0$"
] | |
HW | [
"$\\displaystyle y^{2}-4 y-10=0$"
] | |
HW | [
"$\\displaystyle =22+6 \\sqrt{14}$"
] | |
HW | [
"$\\displaystyle x^{3}=1$"
] | |
HW | [
"$\\displaystyle (x-1)\\left(x^{2}+x+1\\right)=0 .$"
] | |
HW | [
"$\\displaystyle (1) \\; 0 \\;~~~ (2) \\; -1 \\; ~~~(3) \\; 1$"
] | |
HW | [
"$\\displaystyle 9 a>-2916$"
] | |
HW | [
"$\\displaystyle 9 a>-2916$"
] | |
HW | [
"$\\displaystyle -323$"
] | |
HW | [
"$\\displaystyle -323$"
] | |
HW | [
"$\\displaystyle x^{2}+(-6 k-6) x+k^{2}-9=0$"
] | |
HW | [
"$\\displaystyle x^{2}+(-6 k-6) x+k^{2}-9=0$"
] | |
HW | [
"$\\displaystyle k^{2}-9<0$"
] | |
HW | [
"$\\displaystyle (k+3)(k-3)<0$"
] | |
HW | [
"$\\displaystyle (k+3)(k-3)<0$"
] | |
HW | [
"$\\displaystyle -3 < x < 3$"
] | |
HW | [
"$\\displaystyle -3 < x < 3$"
] | |
HW | [
"$\\displaystyle \\left\\{\\begin{array}{l}8 x \\leq 72 \\\\ 2 x-20 \\leq 3 x-k\\end{array}\\right.$"
] | |
HW | [
"$\\displaystyle \\left\\{\\begin{array}{l}x \\leq 9 \\\\ 2 x-3 x \\leq 20-k\\end{array}\\right.$"
] | |
HW | [
"$\\displaystyle -x \\leq 20-k$"
] | |
HW | [
"$\\displaystyle -x \\leq 20-k$"
] | |
HW | [
"$\\displaystyle 29 \\leq k$"
] | |
HW | [
"$\\displaystyle b x-5 a>a x-5 b \\Rightarrow(b-a) x>5(a-b)$"
] | |
HW | [
"$\\displaystyle b x-5 a>a x-5 b \\Rightarrow(b-a) x>5(a-b)$"
] | |
HW | [
"$\\displaystyle x>-5$"
] | |
HW | [
"$\\displaystyle x>-5$"
] | |
HW | [
"$\\displaystyle 9-3 x-4 \\geq x-7$."
] | |
HW | [
"$\\displaystyle 9-3 x-4 \\geq x-7$."
] | |
HW | [
"$\\displaystyle 3 \\geq x$."
] | |
HW | [
"$\\displaystyle 5(-x-5) \\leq 2(2 x+10)$"
] | |
HW | [
"$\\displaystyle 5(-x-5) \\leq 2(2 x+10)$"
] | |
HW | [
"$\\displaystyle -5 x-25 \\leq 4 x+20$"
] | |
HW | [
"$\\displaystyle -5 \\leq x$"
] | |
HW | [
"$\\displaystyle \\therefore-5 \\leq x \\leq 3$"
] | |
HW | [
"$\\displaystyle \\therefore-5 \\leq x \\leq 3$"
] | |
HW | [
"$\\displaystyle a+b=-2$"
] | |
HW | [
"$\\displaystyle a+b=-2$"
] | |
HW | [
"$\\displaystyle -2$"
] | |
HW | [
"$\\displaystyle -2$"
] | |
HW | [
"$\\displaystyle x^{2}=t$"
] | |
HW | [
"$\\displaystyle x^{2}=t$"
] | |
HW | [
"$\\displaystyle (t-5)^{2}=0$"
] | |
HW | [
"$\\displaystyle t=5$"
] | |
HW | [
"$\\displaystyle t=5$"
] | |
HW | [
"$\\displaystyle x^{2}=5$"
] | |
HW | [
"$\\displaystyle x^{2}=5$"
] |
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