Vgln. eerste graad (reeks 4)

Hoofdmenu Eentje per keer  🖨

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

1. \(\frac{x}{3}-\frac{2}{9}=\frac{7}{2}x+7\)
2. \(\frac{x}{3}+\frac{5}{11}=\frac{1}{4}x+8\)
3. \(\frac{x}{3}-\frac{3}{14}=\frac{1}{2}x+8\)
4. \(\frac{x}{4}+\frac{2}{13}=\frac{4}{3}x+4\)
5. \(\frac{x}{5}-\frac{3}{7}=\frac{1}{2}x-2\)
6. \(\frac{x}{7}-\frac{3}{10}=\frac{7}{3}x-2\)
7. \(\frac{x}{3}-\frac{3}{7}=\frac{1}{2}x+6\)
8. \(\frac{x}{6}-\frac{2}{11}=\frac{4}{5}x-2\)
9. \(\frac{x}{7}+\frac{3}{16}=\frac{4}{3}x+5\)
10. \(\frac{x}{3}+\frac{3}{10}=\frac{-2}{5}x+4\)
11. \(\frac{x}{4}+\frac{4}{15}=\frac{3}{5}x-8\)
12. \(\frac{x}{6}-\frac{2}{7}=\frac{2}{5}x+8\)

---

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

1. \(\text{18 is het kleinste gemene veelvoud van 3, 9 en 2} \\ \begin{align} & \frac{x}{3}-\frac{2}{9}& = & \frac{7}{2}x+7 \\\Leftrightarrow & \color{blue}{18.} (\frac{6x}{ \color{blue}{18} }- \frac{ 4 }{ \color{blue}{18} })& = & (\frac{63}{ \color{blue}{18} }x+\frac{126}{ \color{blue}{18} }) \color{blue}{.18} \\\Leftrightarrow & 6x-4& = & 63x+126 \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-63x} & = & \color{red}{63x} +126 \color{blue}{-63x} \color{blue}{+4} \\\Leftrightarrow & -57x& = & 130 \\\Leftrightarrow & \frac{-57x}{ \color{red}{-57} }& = & \frac{130}{-57} \\\Leftrightarrow & x = \frac{-130}{57} & & \\ & V = \left\{ \frac{-130}{57} \right\} & \\\end{align}\)
2. \(\text{132 is het kleinste gemene veelvoud van 3, 11 en 4} \\ \begin{align} & \frac{x}{3}+\frac{5}{11}& = & \frac{1}{4}x+8 \\\Leftrightarrow & \color{blue}{132.} (\frac{44x}{ \color{blue}{132} }+ \frac{ 60 }{ \color{blue}{132} })& = & (\frac{33}{ \color{blue}{132} }x+\frac{1056}{ \color{blue}{132} }) \color{blue}{.132} \\\Leftrightarrow & 44x+60& = & 33x+1056 \\\Leftrightarrow & 44x \color{red}{+60} \color{blue}{-60} \color{blue}{-33x} & = & \color{red}{33x} +1056 \color{blue}{-33x} \color{blue}{-60} \\\Leftrightarrow & 11x& = & 996 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = & \frac{996}{11} \\\Leftrightarrow & x = \frac{996}{11} & & \\ & V = \left\{ \frac{996}{11} \right\} & \\\end{align}\)
3. \(\text{42 is het kleinste gemene veelvoud van 3, 14 en 2} \\ \begin{align} & \frac{x}{3}-\frac{3}{14}& = & \frac{1}{2}x+8 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }- \frac{ 9 }{ \color{blue}{42} })& = & (\frac{21}{ \color{blue}{42} }x+\frac{336}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x-9& = & 21x+336 \\\Leftrightarrow & 14x \color{red}{-9} \color{blue}{+9} \color{blue}{-21x} & = & \color{red}{21x} +336 \color{blue}{-21x} \color{blue}{+9} \\\Leftrightarrow & -7x& = & 345 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = & \frac{345}{-7} \\\Leftrightarrow & x = \frac{-345}{7} & & \\ & V = \left\{ \frac{-345}{7} \right\} & \\\end{align}\)
4. \(\text{156 is het kleinste gemene veelvoud van 4, 13 en 3} \\ \begin{align} & \frac{x}{4}+\frac{2}{13}& = & \frac{4}{3}x+4 \\\Leftrightarrow & \color{blue}{156.} (\frac{39x}{ \color{blue}{156} }+ \frac{ 24 }{ \color{blue}{156} })& = & (\frac{208}{ \color{blue}{156} }x+\frac{624}{ \color{blue}{156} }) \color{blue}{.156} \\\Leftrightarrow & 39x+24& = & 208x+624 \\\Leftrightarrow & 39x \color{red}{+24} \color{blue}{-24} \color{blue}{-208x} & = & \color{red}{208x} +624 \color{blue}{-208x} \color{blue}{-24} \\\Leftrightarrow & -169x& = & 600 \\\Leftrightarrow & \frac{-169x}{ \color{red}{-169} }& = & \frac{600}{-169} \\\Leftrightarrow & x = \frac{-600}{169} & & \\ & V = \left\{ \frac{-600}{169} \right\} & \\\end{align}\)
5. \(\text{70 is het kleinste gemene veelvoud van 5, 7 en 2} \\ \begin{align} & \frac{x}{5}-\frac{3}{7}& = & \frac{1}{2}x-2 \\\Leftrightarrow & \color{blue}{70.} (\frac{14x}{ \color{blue}{70} }- \frac{ 30 }{ \color{blue}{70} })& = & (\frac{35}{ \color{blue}{70} }x-\frac{140}{ \color{blue}{70} }) \color{blue}{.70} \\\Leftrightarrow & 14x-30& = & 35x-140 \\\Leftrightarrow & 14x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} -140 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & -21x& = & -110 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{-110}{-21} \\\Leftrightarrow & x = \frac{110}{21} & & \\ & V = \left\{ \frac{110}{21} \right\} & \\\end{align}\)
6. \(\text{210 is het kleinste gemene veelvoud van 7, 10 en 3} \\ \begin{align} & \frac{x}{7}-\frac{3}{10}& = & \frac{7}{3}x-2 \\\Leftrightarrow & \color{blue}{210.} (\frac{30x}{ \color{blue}{210} }- \frac{ 63 }{ \color{blue}{210} })& = & (\frac{490}{ \color{blue}{210} }x-\frac{420}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 30x-63& = & 490x-420 \\\Leftrightarrow & 30x \color{red}{-63} \color{blue}{+63} \color{blue}{-490x} & = & \color{red}{490x} -420 \color{blue}{-490x} \color{blue}{+63} \\\Leftrightarrow & -460x& = & -357 \\\Leftrightarrow & \frac{-460x}{ \color{red}{-460} }& = & \frac{-357}{-460} \\\Leftrightarrow & x = \frac{357}{460} & & \\ & V = \left\{ \frac{357}{460} \right\} & \\\end{align}\)
7. \(\text{42 is het kleinste gemene veelvoud van 3, 7 en 2} \\ \begin{align} & \frac{x}{3}-\frac{3}{7}& = & \frac{1}{2}x+6 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }- \frac{ 18 }{ \color{blue}{42} })& = & (\frac{21}{ \color{blue}{42} }x+\frac{252}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x-18& = & 21x+252 \\\Leftrightarrow & 14x \color{red}{-18} \color{blue}{+18} \color{blue}{-21x} & = & \color{red}{21x} +252 \color{blue}{-21x} \color{blue}{+18} \\\Leftrightarrow & -7x& = & 270 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = & \frac{270}{-7} \\\Leftrightarrow & x = \frac{-270}{7} & & \\ & V = \left\{ \frac{-270}{7} \right\} & \\\end{align}\)
8. \(\text{330 is het kleinste gemene veelvoud van 6, 11 en 5} \\ \begin{align} & \frac{x}{6}-\frac{2}{11}& = & \frac{4}{5}x-2 \\\Leftrightarrow & \color{blue}{330.} (\frac{55x}{ \color{blue}{330} }- \frac{ 60 }{ \color{blue}{330} })& = & (\frac{264}{ \color{blue}{330} }x-\frac{660}{ \color{blue}{330} }) \color{blue}{.330} \\\Leftrightarrow & 55x-60& = & 264x-660 \\\Leftrightarrow & 55x \color{red}{-60} \color{blue}{+60} \color{blue}{-264x} & = & \color{red}{264x} -660 \color{blue}{-264x} \color{blue}{+60} \\\Leftrightarrow & -209x& = & -600 \\\Leftrightarrow & \frac{-209x}{ \color{red}{-209} }& = & \frac{-600}{-209} \\\Leftrightarrow & x = \frac{600}{209} & & \\ & V = \left\{ \frac{600}{209} \right\} & \\\end{align}\)
9. \(\text{336 is het kleinste gemene veelvoud van 7, 16 en 3} \\ \begin{align} & \frac{x}{7}+\frac{3}{16}& = & \frac{4}{3}x+5 \\\Leftrightarrow & \color{blue}{336.} (\frac{48x}{ \color{blue}{336} }+ \frac{ 63 }{ \color{blue}{336} })& = & (\frac{448}{ \color{blue}{336} }x+\frac{1680}{ \color{blue}{336} }) \color{blue}{.336} \\\Leftrightarrow & 48x+63& = & 448x+1680 \\\Leftrightarrow & 48x \color{red}{+63} \color{blue}{-63} \color{blue}{-448x} & = & \color{red}{448x} +1680 \color{blue}{-448x} \color{blue}{-63} \\\Leftrightarrow & -400x& = & 1617 \\\Leftrightarrow & \frac{-400x}{ \color{red}{-400} }& = & \frac{1617}{-400} \\\Leftrightarrow & x = \frac{-1617}{400} & & \\ & V = \left\{ \frac{-1617}{400} \right\} & \\\end{align}\)
10. \(\text{30 is het kleinste gemene veelvoud van 3, 10 en 5} \\ \begin{align} & \frac{x}{3}+\frac{3}{10}& = & \frac{-2}{5}x+4 \\\Leftrightarrow & \color{blue}{30.} (\frac{10x}{ \color{blue}{30} }+ \frac{ 9 }{ \color{blue}{30} })& = & (\frac{-12}{ \color{blue}{30} }x+\frac{120}{ \color{blue}{30} }) \color{blue}{.30} \\\Leftrightarrow & 10x+9& = & -12x+120 \\\Leftrightarrow & 10x \color{red}{+9} \color{blue}{-9} \color{blue}{+12x} & = & \color{red}{-12x} +120 \color{blue}{+12x} \color{blue}{-9} \\\Leftrightarrow & 22x& = & 111 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = & \frac{111}{22} \\\Leftrightarrow & x = \frac{111}{22} & & \\ & V = \left\{ \frac{111}{22} \right\} & \\\end{align}\)
11. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 5} \\ \begin{align} & \frac{x}{4}+\frac{4}{15}& = & \frac{3}{5}x-8 \\\Leftrightarrow & \color{blue}{60.} (\frac{15x}{ \color{blue}{60} }+ \frac{ 16 }{ \color{blue}{60} })& = & (\frac{36}{ \color{blue}{60} }x-\frac{480}{ \color{blue}{60} }) \color{blue}{.60} \\\Leftrightarrow & 15x+16& = & 36x-480 \\\Leftrightarrow & 15x \color{red}{+16} \color{blue}{-16} \color{blue}{-36x} & = & \color{red}{36x} -480 \color{blue}{-36x} \color{blue}{-16} \\\Leftrightarrow & -21x& = & -496 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{-496}{-21} \\\Leftrightarrow & x = \frac{496}{21} & & \\ & V = \left\{ \frac{496}{21} \right\} & \\\end{align}\)
12. \(\text{210 is het kleinste gemene veelvoud van 6, 7 en 5} \\ \begin{align} & \frac{x}{6}-\frac{2}{7}& = & \frac{2}{5}x+8 \\\Leftrightarrow & \color{blue}{210.} (\frac{35x}{ \color{blue}{210} }- \frac{ 60 }{ \color{blue}{210} })& = & (\frac{84}{ \color{blue}{210} }x+\frac{1680}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 35x-60& = & 84x+1680 \\\Leftrightarrow & 35x \color{red}{-60} \color{blue}{+60} \color{blue}{-84x} & = & \color{red}{84x} +1680 \color{blue}{-84x} \color{blue}{+60} \\\Leftrightarrow & -49x& = & 1740 \\\Leftrightarrow & \frac{-49x}{ \color{red}{-49} }& = & \frac{1740}{-49} \\\Leftrightarrow & x = \frac{-1740}{49} & & \\ & V = \left\{ \frac{-1740}{49} \right\} & \\\end{align}\)