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. \(\frac{x}{3}-\frac{3}{8}=\frac{3}{4}x+7\)
  2. \(\frac{x}{5}-\frac{4}{11}=\frac{-3}{7}x-1\)
  3. \(\frac{x}{2}+\frac{5}{16}=\frac{2}{3}x-4\)
  4. \(\frac{x}{7}-\frac{5}{11}=\frac{1}{2}x-8\)
  5. \(\frac{x}{2}-\frac{2}{9}=\frac{3}{7}x+8\)
  6. \(\frac{x}{3}-\frac{2}{17}=\frac{7}{2}x+2\)
  7. \(\frac{x}{4}-\frac{3}{16}=\frac{4}{7}x-7\)
  8. \(\frac{x}{6}+\frac{5}{8}=\frac{-7}{5}x+2\)
  9. \(\frac{x}{2}-\frac{5}{6}=\frac{6}{7}x+1\)
  10. \(\frac{x}{6}-\frac{5}{9}=\frac{8}{5}x-4\)
  11. \(\frac{x}{3}+\frac{2}{9}=\frac{3}{2}x+1\)
  12. \(\frac{x}{7}-\frac{3}{13}=\frac{1}{2}x+3\)

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

Verbetersleutel

  1. \(\text{24 is het kleinste gemene veelvoud van 3, 8 en 4} \\ \begin{align} & \color{blue}{24.} (\frac{x}{3}-\frac{3}{8})& = & (\frac{3}{4}x+7) \color{blue}{.24} \\\Leftrightarrow & 8x-9& = & 18x+168 \\\Leftrightarrow & 8x \color{red}{-9} \color{blue}{+9} \color{blue}{-18x} & = & \color{red}{18x} +168 \color{blue}{-18x} \color{blue}{+9} \\\Leftrightarrow & -10x& = & 177 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = & \frac{177}{-10} \\\Leftrightarrow & x = \frac{-177}{10} & & \\ & V = \left\{ \frac{-177}{10} \right\} & \\\end{align}\)
  2. \(\text{385 is het kleinste gemene veelvoud van 5, 11 en 7} \\ \begin{align} & \color{blue}{385.} (\frac{x}{5}-\frac{4}{11})& = & (\frac{-3}{7}x-1) \color{blue}{.385} \\\Leftrightarrow & 77x-140& = & -165x-385 \\\Leftrightarrow & 77x \color{red}{-140} \color{blue}{+140} \color{blue}{+165x} & = & \color{red}{-165x} -385 \color{blue}{+165x} \color{blue}{+140} \\\Leftrightarrow & 242x& = & -245 \\\Leftrightarrow & \frac{242x}{ \color{red}{242} }& = & \frac{-245}{242} \\\Leftrightarrow & x = \frac{-245}{242} & & \\ & V = \left\{ \frac{-245}{242} \right\} & \\\end{align}\)
  3. \(\text{48 is het kleinste gemene veelvoud van 2, 16 en 3} \\ \begin{align} & \color{blue}{48.} (\frac{x}{2}+\frac{5}{16})& = & (\frac{2}{3}x-4) \color{blue}{.48} \\\Leftrightarrow & 24x+15& = & 32x-192 \\\Leftrightarrow & 24x \color{red}{+15} \color{blue}{-15} \color{blue}{-32x} & = & \color{red}{32x} -192 \color{blue}{-32x} \color{blue}{-15} \\\Leftrightarrow & -8x& = & -207 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = & \frac{-207}{-8} \\\Leftrightarrow & x = \frac{207}{8} & & \\ & V = \left\{ \frac{207}{8} \right\} & \\\end{align}\)
  4. \(\text{154 is het kleinste gemene veelvoud van 7, 11 en 2} \\ \begin{align} & \color{blue}{154.} (\frac{x}{7}-\frac{5}{11})& = & (\frac{1}{2}x-8) \color{blue}{.154} \\\Leftrightarrow & 22x-70& = & 77x-1232 \\\Leftrightarrow & 22x \color{red}{-70} \color{blue}{+70} \color{blue}{-77x} & = & \color{red}{77x} -1232 \color{blue}{-77x} \color{blue}{+70} \\\Leftrightarrow & -55x& = & -1162 \\\Leftrightarrow & \frac{-55x}{ \color{red}{-55} }& = & \frac{-1162}{-55} \\\Leftrightarrow & x = \frac{1162}{55} & & \\ & V = \left\{ \frac{1162}{55} \right\} & \\\end{align}\)
  5. \(\text{126 is het kleinste gemene veelvoud van 2, 9 en 7} \\ \begin{align} & \color{blue}{126.} (\frac{x}{2}-\frac{2}{9})& = & (\frac{3}{7}x+8) \color{blue}{.126} \\\Leftrightarrow & 63x-28& = & 54x+1008 \\\Leftrightarrow & 63x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +1008 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & 9x& = & 1036 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = & \frac{1036}{9} \\\Leftrightarrow & x = \frac{1036}{9} & & \\ & V = \left\{ \frac{1036}{9} \right\} & \\\end{align}\)
  6. \(\text{102 is het kleinste gemene veelvoud van 3, 17 en 2} \\ \begin{align} & \color{blue}{102.} (\frac{x}{3}-\frac{2}{17})& = & (\frac{7}{2}x+2) \color{blue}{.102} \\\Leftrightarrow & 34x-12& = & 357x+204 \\\Leftrightarrow & 34x \color{red}{-12} \color{blue}{+12} \color{blue}{-357x} & = & \color{red}{357x} +204 \color{blue}{-357x} \color{blue}{+12} \\\Leftrightarrow & -323x& = & 216 \\\Leftrightarrow & \frac{-323x}{ \color{red}{-323} }& = & \frac{216}{-323} \\\Leftrightarrow & x = \frac{-216}{323} & & \\ & V = \left\{ \frac{-216}{323} \right\} & \\\end{align}\)
  7. \(\text{112 is het kleinste gemene veelvoud van 4, 16 en 7} \\ \begin{align} & \color{blue}{112.} (\frac{x}{4}-\frac{3}{16})& = & (\frac{4}{7}x-7) \color{blue}{.112} \\\Leftrightarrow & 28x-21& = & 64x-784 \\\Leftrightarrow & 28x \color{red}{-21} \color{blue}{+21} \color{blue}{-64x} & = & \color{red}{64x} -784 \color{blue}{-64x} \color{blue}{+21} \\\Leftrightarrow & -36x& = & -763 \\\Leftrightarrow & \frac{-36x}{ \color{red}{-36} }& = & \frac{-763}{-36} \\\Leftrightarrow & x = \frac{763}{36} & & \\ & V = \left\{ \frac{763}{36} \right\} & \\\end{align}\)
  8. \(\text{120 is het kleinste gemene veelvoud van 6, 8 en 5} \\ \begin{align} & \color{blue}{120.} (\frac{x}{6}+\frac{5}{8})& = & (\frac{-7}{5}x+2) \color{blue}{.120} \\\Leftrightarrow & 20x+75& = & -168x+240 \\\Leftrightarrow & 20x \color{red}{+75} \color{blue}{-75} \color{blue}{+168x} & = & \color{red}{-168x} +240 \color{blue}{+168x} \color{blue}{-75} \\\Leftrightarrow & 188x& = & 165 \\\Leftrightarrow & \frac{188x}{ \color{red}{188} }& = & \frac{165}{188} \\\Leftrightarrow & x = \frac{165}{188} & & \\ & V = \left\{ \frac{165}{188} \right\} & \\\end{align}\)
  9. \(\text{42 is het kleinste gemene veelvoud van 2, 6 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{2}-\frac{5}{6})& = & (\frac{6}{7}x+1) \color{blue}{.42} \\\Leftrightarrow & 21x-35& = & 36x+42 \\\Leftrightarrow & 21x \color{red}{-35} \color{blue}{+35} \color{blue}{-36x} & = & \color{red}{36x} +42 \color{blue}{-36x} \color{blue}{+35} \\\Leftrightarrow & -15x& = & 77 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = & \frac{77}{-15} \\\Leftrightarrow & x = \frac{-77}{15} & & \\ & V = \left\{ \frac{-77}{15} \right\} & \\\end{align}\)
  10. \(\text{90 is het kleinste gemene veelvoud van 6, 9 en 5} \\ \begin{align} & \color{blue}{90.} (\frac{x}{6}-\frac{5}{9})& = & (\frac{8}{5}x-4) \color{blue}{.90} \\\Leftrightarrow & 15x-50& = & 144x-360 \\\Leftrightarrow & 15x \color{red}{-50} \color{blue}{+50} \color{blue}{-144x} & = & \color{red}{144x} -360 \color{blue}{-144x} \color{blue}{+50} \\\Leftrightarrow & -129x& = & -310 \\\Leftrightarrow & \frac{-129x}{ \color{red}{-129} }& = & \frac{-310}{-129} \\\Leftrightarrow & x = \frac{310}{129} & & \\ & V = \left\{ \frac{310}{129} \right\} & \\\end{align}\)
  11. \(\text{18 is het kleinste gemene veelvoud van 3, 9 en 2} \\ \begin{align} & \color{blue}{18.} (\frac{x}{3}+\frac{2}{9})& = & (\frac{3}{2}x+1) \color{blue}{.18} \\\Leftrightarrow & 6x+4& = & 27x+18 \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{-27x} & = & \color{red}{27x} +18 \color{blue}{-27x} \color{blue}{-4} \\\Leftrightarrow & -21x& = & 14 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{14}{-21} \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
  12. \(\text{182 is het kleinste gemene veelvoud van 7, 13 en 2} \\ \begin{align} & \color{blue}{182.} (\frac{x}{7}-\frac{3}{13})& = & (\frac{1}{2}x+3) \color{blue}{.182} \\\Leftrightarrow & 26x-42& = & 91x+546 \\\Leftrightarrow & 26x \color{red}{-42} \color{blue}{+42} \color{blue}{-91x} & = & \color{red}{91x} +546 \color{blue}{-91x} \color{blue}{+42} \\\Leftrightarrow & -65x& = & 588 \\\Leftrightarrow & \frac{-65x}{ \color{red}{-65} }& = & \frac{588}{-65} \\\Leftrightarrow & x = \frac{-588}{65} & & \\ & V = \left\{ \frac{-588}{65} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 05:55:13