Vgln. eerste graad (reeks 4)

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

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

Verbetersleutel

1. \(\text{48 is het kleinste gemene veelvoud van 3, 16 en 2} \\ \begin{align} & \frac{x}{3}-\frac{3}{16}& = & \frac{7}{2}x+6 \\\Leftrightarrow & \color{blue}{48.} (\frac{16x}{ \color{blue}{48} }- \frac{ 9 }{ \color{blue}{48} })& = & (\frac{168}{ \color{blue}{48} }x+\frac{288}{ \color{blue}{48} }) \color{blue}{.48} \\\Leftrightarrow & 16x-9& = & 168x+288 \\\Leftrightarrow & 16x \color{red}{-9} \color{blue}{+9} \color{blue}{-168x} & = & \color{red}{168x} +288 \color{blue}{-168x} \color{blue}{+9} \\\Leftrightarrow & -152x& = & 297 \\\Leftrightarrow & \frac{-152x}{ \color{red}{-152} }& = & \frac{297}{-152} \\\Leftrightarrow & x = \frac{-297}{152} & & \\ & V = \left\{ \frac{-297}{152} \right\} & \\\end{align}\)
2. \(\text{42 is het kleinste gemene veelvoud van 2, 7 en 3} \\ \begin{align} & \frac{x}{2}+\frac{4}{7}& = & \frac{4}{3}x+6 \\\Leftrightarrow & \color{blue}{42.} (\frac{21x}{ \color{blue}{42} }+ \frac{ 24 }{ \color{blue}{42} })& = & (\frac{56}{ \color{blue}{42} }x+\frac{252}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 21x+24& = & 56x+252 \\\Leftrightarrow & 21x \color{red}{+24} \color{blue}{-24} \color{blue}{-56x} & = & \color{red}{56x} +252 \color{blue}{-56x} \color{blue}{-24} \\\Leftrightarrow & -35x& = & 228 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = & \frac{228}{-35} \\\Leftrightarrow & x = \frac{-228}{35} & & \\ & V = \left\{ \frac{-228}{35} \right\} & \\\end{align}\)
3. \(\text{330 is het kleinste gemene veelvoud van 6, 11 en 5} \\ \begin{align} & \frac{x}{6}+\frac{2}{11}& = & \frac{1}{5}x-2 \\\Leftrightarrow & \color{blue}{330.} (\frac{55x}{ \color{blue}{330} }+ \frac{ 60 }{ \color{blue}{330} })& = & (\frac{66}{ \color{blue}{330} }x-\frac{660}{ \color{blue}{330} }) \color{blue}{.330} \\\Leftrightarrow & 55x+60& = & 66x-660 \\\Leftrightarrow & 55x \color{red}{+60} \color{blue}{-60} \color{blue}{-66x} & = & \color{red}{66x} -660 \color{blue}{-66x} \color{blue}{-60} \\\Leftrightarrow & -11x& = & -720 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = & \frac{-720}{-11} \\\Leftrightarrow & x = \frac{720}{11} & & \\ & V = \left\{ \frac{720}{11} \right\} & \\\end{align}\)
4. \(\text{70 is het kleinste gemene veelvoud van 2, 14 en 5} \\ \begin{align} & \frac{x}{2}-\frac{3}{14}& = & \frac{1}{5}x+5 \\\Leftrightarrow & \color{blue}{70.} (\frac{35x}{ \color{blue}{70} }- \frac{ 15 }{ \color{blue}{70} })& = & (\frac{14}{ \color{blue}{70} }x+\frac{350}{ \color{blue}{70} }) \color{blue}{.70} \\\Leftrightarrow & 35x-15& = & 14x+350 \\\Leftrightarrow & 35x \color{red}{-15} \color{blue}{+15} \color{blue}{-14x} & = & \color{red}{14x} +350 \color{blue}{-14x} \color{blue}{+15} \\\Leftrightarrow & 21x& = & 365 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = & \frac{365}{21} \\\Leftrightarrow & x = \frac{365}{21} & & \\ & V = \left\{ \frac{365}{21} \right\} & \\\end{align}\)
5. \(\text{40 is het kleinste gemene veelvoud van 2, 8 en 5} \\ \begin{align} & \frac{x}{2}-\frac{5}{8}& = & \frac{-7}{5}x-6 \\\Leftrightarrow & \color{blue}{40.} (\frac{20x}{ \color{blue}{40} }- \frac{ 25 }{ \color{blue}{40} })& = & (\frac{-56}{ \color{blue}{40} }x-\frac{240}{ \color{blue}{40} }) \color{blue}{.40} \\\Leftrightarrow & 20x-25& = & -56x-240 \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+56x} & = & \color{red}{-56x} -240 \color{blue}{+56x} \color{blue}{+25} \\\Leftrightarrow & 76x& = & -215 \\\Leftrightarrow & \frac{76x}{ \color{red}{76} }& = & \frac{-215}{76} \\\Leftrightarrow & x = \frac{-215}{76} & & \\ & V = \left\{ \frac{-215}{76} \right\} & \\\end{align}\)
6. \(\text{42 is het kleinste gemene veelvoud van 3, 7 en 2} \\ \begin{align} & \frac{x}{3}-\frac{2}{7}& = & \frac{1}{2}x+8 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }- \frac{ 12 }{ \color{blue}{42} })& = & (\frac{21}{ \color{blue}{42} }x+\frac{336}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x-12& = & 21x+336 \\\Leftrightarrow & 14x \color{red}{-12} \color{blue}{+12} \color{blue}{-21x} & = & \color{red}{21x} +336 \color{blue}{-21x} \color{blue}{+12} \\\Leftrightarrow & -7x& = & 348 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = & \frac{348}{-7} \\\Leftrightarrow & x = \frac{-348}{7} & & \\ & V = \left\{ \frac{-348}{7} \right\} & \\\end{align}\)
7. \(\text{132 is het kleinste gemene veelvoud van 3, 11 en 4} \\ \begin{align} & \frac{x}{3}-\frac{4}{11}& = & \frac{1}{4}x+7 \\\Leftrightarrow & \color{blue}{132.} (\frac{44x}{ \color{blue}{132} }- \frac{ 48 }{ \color{blue}{132} })& = & (\frac{33}{ \color{blue}{132} }x+\frac{924}{ \color{blue}{132} }) \color{blue}{.132} \\\Leftrightarrow & 44x-48& = & 33x+924 \\\Leftrightarrow & 44x \color{red}{-48} \color{blue}{+48} \color{blue}{-33x} & = & \color{red}{33x} +924 \color{blue}{-33x} \color{blue}{+48} \\\Leftrightarrow & 11x& = & 972 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = & \frac{972}{11} \\\Leftrightarrow & x = \frac{972}{11} & & \\ & V = \left\{ \frac{972}{11} \right\} & \\\end{align}\)
8. \(\text{60 is het kleinste gemene veelvoud van 3, 15 en 4} \\ \begin{align} & \frac{x}{3}-\frac{4}{15}& = & \frac{-3}{4}x-4 \\\Leftrightarrow & \color{blue}{60.} (\frac{20x}{ \color{blue}{60} }- \frac{ 16 }{ \color{blue}{60} })& = & (\frac{-45}{ \color{blue}{60} }x-\frac{240}{ \color{blue}{60} }) \color{blue}{.60} \\\Leftrightarrow & 20x-16& = & -45x-240 \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+45x} & = & \color{red}{-45x} -240 \color{blue}{+45x} \color{blue}{+16} \\\Leftrightarrow & 65x& = & -224 \\\Leftrightarrow & \frac{65x}{ \color{red}{65} }& = & \frac{-224}{65} \\\Leftrightarrow & x = \frac{-224}{65} & & \\ & V = \left\{ \frac{-224}{65} \right\} & \\\end{align}\)
9. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 5} \\ \begin{align} & \frac{x}{4}-\frac{2}{15}& = & \frac{-4}{5}x+6 \\\Leftrightarrow & \color{blue}{60.} (\frac{15x}{ \color{blue}{60} }- \frac{ 8 }{ \color{blue}{60} })& = & (\frac{-48}{ \color{blue}{60} }x+\frac{360}{ \color{blue}{60} }) \color{blue}{.60} \\\Leftrightarrow & 15x-8& = & -48x+360 \\\Leftrightarrow & 15x \color{red}{-8} \color{blue}{+8} \color{blue}{+48x} & = & \color{red}{-48x} +360 \color{blue}{+48x} \color{blue}{+8} \\\Leftrightarrow & 63x& = & 368 \\\Leftrightarrow & \frac{63x}{ \color{red}{63} }& = & \frac{368}{63} \\\Leftrightarrow & x = \frac{368}{63} & & \\ & V = \left\{ \frac{368}{63} \right\} & \\\end{align}\)
10. \(\text{156 is het kleinste gemene veelvoud van 3, 13 en 4} \\ \begin{align} & \frac{x}{3}+\frac{2}{13}& = & \frac{-7}{4}x+3 \\\Leftrightarrow & \color{blue}{156.} (\frac{52x}{ \color{blue}{156} }+ \frac{ 24 }{ \color{blue}{156} })& = & (\frac{-273}{ \color{blue}{156} }x+\frac{468}{ \color{blue}{156} }) \color{blue}{.156} \\\Leftrightarrow & 52x+24& = & -273x+468 \\\Leftrightarrow & 52x \color{red}{+24} \color{blue}{-24} \color{blue}{+273x} & = & \color{red}{-273x} +468 \color{blue}{+273x} \color{blue}{-24} \\\Leftrightarrow & 325x& = & 444 \\\Leftrightarrow & \frac{325x}{ \color{red}{325} }& = & \frac{444}{325} \\\Leftrightarrow & x = \frac{444}{325} & & \\ & V = \left\{ \frac{444}{325} \right\} & \\\end{align}\)
11. \(\text{42 is het kleinste gemene veelvoud van 3, 7 en 2} \\ \begin{align} & \frac{x}{3}+\frac{4}{7}& = & \frac{1}{2}x-6 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }+ \frac{ 24 }{ \color{blue}{42} })& = & (\frac{21}{ \color{blue}{42} }x-\frac{252}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x+24& = & 21x-252 \\\Leftrightarrow & 14x \color{red}{+24} \color{blue}{-24} \color{blue}{-21x} & = & \color{red}{21x} -252 \color{blue}{-21x} \color{blue}{-24} \\\Leftrightarrow & -7x& = & -276 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = & \frac{-276}{-7} \\\Leftrightarrow & x = \frac{276}{7} & & \\ & V = \left\{ \frac{276}{7} \right\} & \\\end{align}\)
12. \(\text{210 is het kleinste gemene veelvoud van 7, 15 en 6} \\ \begin{align} & \frac{x}{7}+\frac{2}{15}& = & \frac{1}{6}x+8 \\\Leftrightarrow & \color{blue}{210.} (\frac{30x}{ \color{blue}{210} }+ \frac{ 28 }{ \color{blue}{210} })& = & (\frac{35}{ \color{blue}{210} }x+\frac{1680}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 30x+28& = & 35x+1680 \\\Leftrightarrow & 30x \color{red}{+28} \color{blue}{-28} \color{blue}{-35x} & = & \color{red}{35x} +1680 \color{blue}{-35x} \color{blue}{-28} \\\Leftrightarrow & -5x& = & 1652 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = & \frac{1652}{-5} \\\Leftrightarrow & x = \frac{-1652}{5} & & \\ & V = \left\{ \frac{-1652}{5} \right\} & \\\end{align}\)