Vgln. eerste graad (reeks 4)

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

  1. \(\frac{x}{2}+\frac{3}{11}=\frac{-3}{7}x-8\)
  2. \(\frac{x}{5}+\frac{5}{6}=\frac{6}{7}x+2\)
  3. \(\frac{x}{4}+\frac{5}{12}=\frac{2}{3}x-8\)
  4. \(\frac{x}{5}-\frac{4}{17}=\frac{8}{3}x-8\)
  5. \(\frac{x}{4}-\frac{2}{15}=\frac{2}{7}x-7\)
  6. \(\frac{x}{4}-\frac{4}{9}=\frac{-7}{5}x+5\)
  7. \(\frac{x}{6}+\frac{4}{13}=\frac{1}{5}x+6\)
  8. \(\frac{x}{5}-\frac{4}{7}=\frac{7}{2}x-8\)
  9. \(\frac{x}{4}-\frac{2}{7}=\frac{-2}{3}x-3\)
  10. \(\frac{x}{5}-\frac{4}{13}=\frac{-3}{4}x-8\)
  11. \(\frac{x}{7}-\frac{5}{7}=\frac{7}{4}x-1\)
  12. \(\frac{x}{7}+\frac{4}{7}=\frac{3}{2}x-6\)

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

Verbetersleutel

  1. \(\text{154 is het kleinste gemene veelvoud van 2, 11 en 7} \\ \begin{align} & \color{blue}{154.} (\frac{x}{2}+\frac{3}{11})& = & (\frac{-3}{7}x-8) \color{blue}{.154} \\\Leftrightarrow & 77x+42& = & -66x-1232 \\\Leftrightarrow & 77x \color{red}{+42} \color{blue}{-42} \color{blue}{+66x} & = & \color{red}{-66x} -1232 \color{blue}{+66x} \color{blue}{-42} \\\Leftrightarrow & 143x& = & -1274 \\\Leftrightarrow & \frac{143x}{ \color{red}{143} }& = & \frac{-1274}{143} \\\Leftrightarrow & x = \frac{-98}{11} & & \\ & V = \left\{ \frac{-98}{11} \right\} & \\\end{align}\)
  2. \(\text{210 is het kleinste gemene veelvoud van 5, 6 en 7} \\ \begin{align} & \color{blue}{210.} (\frac{x}{5}+\frac{5}{6})& = & (\frac{6}{7}x+2) \color{blue}{.210} \\\Leftrightarrow & 42x+175& = & 180x+420 \\\Leftrightarrow & 42x \color{red}{+175} \color{blue}{-175} \color{blue}{-180x} & = & \color{red}{180x} +420 \color{blue}{-180x} \color{blue}{-175} \\\Leftrightarrow & -138x& = & 245 \\\Leftrightarrow & \frac{-138x}{ \color{red}{-138} }& = & \frac{245}{-138} \\\Leftrightarrow & x = \frac{-245}{138} & & \\ & V = \left\{ \frac{-245}{138} \right\} & \\\end{align}\)
  3. \(\text{12 is het kleinste gemene veelvoud van 4, 12 en 3} \\ \begin{align} & \color{blue}{12.} (\frac{x}{4}+\frac{5}{12})& = & (\frac{2}{3}x-8) \color{blue}{.12} \\\Leftrightarrow & 3x+5& = & 8x-96 \\\Leftrightarrow & 3x \color{red}{+5} \color{blue}{-5} \color{blue}{-8x} & = & \color{red}{8x} -96 \color{blue}{-8x} \color{blue}{-5} \\\Leftrightarrow & -5x& = & -101 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = & \frac{-101}{-5} \\\Leftrightarrow & x = \frac{101}{5} & & \\ & V = \left\{ \frac{101}{5} \right\} & \\\end{align}\)
  4. \(\text{255 is het kleinste gemene veelvoud van 5, 17 en 3} \\ \begin{align} & \color{blue}{255.} (\frac{x}{5}-\frac{4}{17})& = & (\frac{8}{3}x-8) \color{blue}{.255} \\\Leftrightarrow & 51x-60& = & 680x-2040 \\\Leftrightarrow & 51x \color{red}{-60} \color{blue}{+60} \color{blue}{-680x} & = & \color{red}{680x} -2040 \color{blue}{-680x} \color{blue}{+60} \\\Leftrightarrow & -629x& = & -1980 \\\Leftrightarrow & \frac{-629x}{ \color{red}{-629} }& = & \frac{-1980}{-629} \\\Leftrightarrow & x = \frac{1980}{629} & & \\ & V = \left\{ \frac{1980}{629} \right\} & \\\end{align}\)
  5. \(\text{420 is het kleinste gemene veelvoud van 4, 15 en 7} \\ \begin{align} & \color{blue}{420.} (\frac{x}{4}-\frac{2}{15})& = & (\frac{2}{7}x-7) \color{blue}{.420} \\\Leftrightarrow & 105x-56& = & 120x-2940 \\\Leftrightarrow & 105x \color{red}{-56} \color{blue}{+56} \color{blue}{-120x} & = & \color{red}{120x} -2940 \color{blue}{-120x} \color{blue}{+56} \\\Leftrightarrow & -15x& = & -2884 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = & \frac{-2884}{-15} \\\Leftrightarrow & x = \frac{2884}{15} & & \\ & V = \left\{ \frac{2884}{15} \right\} & \\\end{align}\)
  6. \(\text{180 is het kleinste gemene veelvoud van 4, 9 en 5} \\ \begin{align} & \color{blue}{180.} (\frac{x}{4}-\frac{4}{9})& = & (\frac{-7}{5}x+5) \color{blue}{.180} \\\Leftrightarrow & 45x-80& = & -252x+900 \\\Leftrightarrow & 45x \color{red}{-80} \color{blue}{+80} \color{blue}{+252x} & = & \color{red}{-252x} +900 \color{blue}{+252x} \color{blue}{+80} \\\Leftrightarrow & 297x& = & 980 \\\Leftrightarrow & \frac{297x}{ \color{red}{297} }& = & \frac{980}{297} \\\Leftrightarrow & x = \frac{980}{297} & & \\ & V = \left\{ \frac{980}{297} \right\} & \\\end{align}\)
  7. \(\text{390 is het kleinste gemene veelvoud van 6, 13 en 5} \\ \begin{align} & \color{blue}{390.} (\frac{x}{6}+\frac{4}{13})& = & (\frac{1}{5}x+6) \color{blue}{.390} \\\Leftrightarrow & 65x+120& = & 78x+2340 \\\Leftrightarrow & 65x \color{red}{+120} \color{blue}{-120} \color{blue}{-78x} & = & \color{red}{78x} +2340 \color{blue}{-78x} \color{blue}{-120} \\\Leftrightarrow & -13x& = & 2220 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = & \frac{2220}{-13} \\\Leftrightarrow & x = \frac{-2220}{13} & & \\ & V = \left\{ \frac{-2220}{13} \right\} & \\\end{align}\)
  8. \(\text{70 is het kleinste gemene veelvoud van 5, 7 en 2} \\ \begin{align} & \color{blue}{70.} (\frac{x}{5}-\frac{4}{7})& = & (\frac{7}{2}x-8) \color{blue}{.70} \\\Leftrightarrow & 14x-40& = & 245x-560 \\\Leftrightarrow & 14x \color{red}{-40} \color{blue}{+40} \color{blue}{-245x} & = & \color{red}{245x} -560 \color{blue}{-245x} \color{blue}{+40} \\\Leftrightarrow & -231x& = & -520 \\\Leftrightarrow & \frac{-231x}{ \color{red}{-231} }& = & \frac{-520}{-231} \\\Leftrightarrow & x = \frac{520}{231} & & \\ & V = \left\{ \frac{520}{231} \right\} & \\\end{align}\)
  9. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \color{blue}{84.} (\frac{x}{4}-\frac{2}{7})& = & (\frac{-2}{3}x-3) \color{blue}{.84} \\\Leftrightarrow & 21x-24& = & -56x-252 \\\Leftrightarrow & 21x \color{red}{-24} \color{blue}{+24} \color{blue}{+56x} & = & \color{red}{-56x} -252 \color{blue}{+56x} \color{blue}{+24} \\\Leftrightarrow & 77x& = & -228 \\\Leftrightarrow & \frac{77x}{ \color{red}{77} }& = & \frac{-228}{77} \\\Leftrightarrow & x = \frac{-228}{77} & & \\ & V = \left\{ \frac{-228}{77} \right\} & \\\end{align}\)
  10. \(\text{260 is het kleinste gemene veelvoud van 5, 13 en 4} \\ \begin{align} & \color{blue}{260.} (\frac{x}{5}-\frac{4}{13})& = & (\frac{-3}{4}x-8) \color{blue}{.260} \\\Leftrightarrow & 52x-80& = & -195x-2080 \\\Leftrightarrow & 52x \color{red}{-80} \color{blue}{+80} \color{blue}{+195x} & = & \color{red}{-195x} -2080 \color{blue}{+195x} \color{blue}{+80} \\\Leftrightarrow & 247x& = & -2000 \\\Leftrightarrow & \frac{247x}{ \color{red}{247} }& = & \frac{-2000}{247} \\\Leftrightarrow & x = \frac{-2000}{247} & & \\ & V = \left\{ \frac{-2000}{247} \right\} & \\\end{align}\)
  11. \(\text{28 is het kleinste gemene veelvoud van 7, 7 en 4} \\ \begin{align} & \color{blue}{28.} (\frac{x}{7}-\frac{5}{7})& = & (\frac{7}{4}x-1) \color{blue}{.28} \\\Leftrightarrow & 4x-20& = & 49x-28 \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} -28 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & -45x& = & -8 \\\Leftrightarrow & \frac{-45x}{ \color{red}{-45} }& = & \frac{-8}{-45} \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
  12. \(\text{14 is het kleinste gemene veelvoud van 7, 7 en 2} \\ \begin{align} & \color{blue}{14.} (\frac{x}{7}+\frac{4}{7})& = & (\frac{3}{2}x-6) \color{blue}{.14} \\\Leftrightarrow & 2x+8& = & 21x-84 \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} -84 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -19x& = & -92 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = & \frac{-92}{-19} \\\Leftrightarrow & x = \frac{92}{19} & & \\ & V = \left\{ \frac{92}{19} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-08-18 12:50:38