Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{13})& = & 13x+\frac{2}{11} \\\Leftrightarrow & 14x+\frac{14}{13}& = & 13x+\frac{2}{11} \\ & & & \text{kgv van noemers 13 en 11 is 143} \\\Leftrightarrow & \color{blue}{143} .(14x+\frac{14}{13})& = & (13x+\frac{2}{11}). \color{blue}{143} \\\Leftrightarrow & 2002x \color{red}{+154} & = & \color{red}{1859x} +26 \\\Leftrightarrow & 2002x \color{red}{+154} \color{blue}{-154} \color{blue}{-1859x} & = & \color{red}{1859x} +26 \color{blue}{-1859x} \color{blue}{-154} \\\Leftrightarrow & 2002x-1859x& = & 26-154 \\\Leftrightarrow & \color{red}{143} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{143} & & \\ & V = \left\{ \frac{-128}{143} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{13})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{12}{13}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 13 en 12 is 156} \\\Leftrightarrow & \color{blue}{156} .(12x+\frac{12}{13})& = & (5x+\frac{7}{12}). \color{blue}{156} \\\Leftrightarrow & 1872x \color{red}{+144} & = & \color{red}{780x} +91 \\\Leftrightarrow & 1872x \color{red}{+144} \color{blue}{-144} \color{blue}{-780x} & = & \color{red}{780x} +91 \color{blue}{-780x} \color{blue}{-144} \\\Leftrightarrow & 1872x-780x& = & 91-144 \\\Leftrightarrow & \color{red}{1092} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{1092} & & \\ & V = \left\{ \frac{-53}{1092} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-x-\frac{3}{8})& = & -4x+\frac{2}{7} \\\Leftrightarrow & -x-\frac{3}{8}& = & -4x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(-x-\frac{3}{8})& = & (-4x+\frac{2}{7}). \color{blue}{56} \\\Leftrightarrow & -56x \color{red}{-21} & = & \color{red}{-224x} +16 \\\Leftrightarrow & -56x \color{red}{-21} \color{blue}{+21} \color{blue}{+224x} & = & \color{red}{-224x} +16 \color{blue}{+224x} \color{blue}{+21} \\\Leftrightarrow & -56x+224x& = & 16+21 \\\Leftrightarrow & \color{red}{168} x& = & 37 \\\Leftrightarrow & x = \frac{37}{168} & & \\ & V = \left\{ \frac{37}{168} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{2})& = & 8x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{15}{2}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(15x-\frac{15}{2})& = & (8x+\frac{8}{5}). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-75} & = & \color{red}{80x} +16 \\\Leftrightarrow & 150x \color{red}{-75} \color{blue}{+75} \color{blue}{-80x} & = & \color{red}{80x} +16 \color{blue}{-80x} \color{blue}{+75} \\\Leftrightarrow & 150x-80x& = & 16+75 \\\Leftrightarrow & \color{red}{70} x& = & 91 \\\Leftrightarrow & x = \frac{91}{70} & & \\\Leftrightarrow & x = \frac{13}{10} & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (x+\frac{4}{13})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 4x+\frac{16}{13}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 13 en 5 is 65} \\\Leftrightarrow & \color{blue}{65} .(4x+\frac{16}{13})& = & (7x+\frac{8}{5}). \color{blue}{65} \\\Leftrightarrow & 260x \color{red}{+80} & = & \color{red}{455x} +104 \\\Leftrightarrow & 260x \color{red}{+80} \color{blue}{-80} \color{blue}{-455x} & = & \color{red}{455x} +104 \color{blue}{-455x} \color{blue}{-80} \\\Leftrightarrow & 260x-455x& = & 104-80 \\\Leftrightarrow & \color{red}{-195} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-195} & & \\\Leftrightarrow & x = \frac{-8}{65} & & \\ & V = \left\{ \frac{-8}{65} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (3x-\frac{5}{11})& = & 5x+\frac{8}{15} \\\Leftrightarrow & 3x-\frac{5}{11}& = & 5x+\frac{8}{15} \\ & & & \text{kgv van noemers 11 en 15 is 165} \\\Leftrightarrow & \color{blue}{165} .(3x-\frac{5}{11})& = & (5x+\frac{8}{15}). \color{blue}{165} \\\Leftrightarrow & 495x \color{red}{-75} & = & \color{red}{825x} +88 \\\Leftrightarrow & 495x \color{red}{-75} \color{blue}{+75} \color{blue}{-825x} & = & \color{red}{825x} +88 \color{blue}{-825x} \color{blue}{+75} \\\Leftrightarrow & 495x-825x& = & 88+75 \\\Leftrightarrow & \color{red}{-330} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-330} & & \\\Leftrightarrow & x = \frac{-163}{330} & & \\ & V = \left\{ \frac{-163}{330} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{2})& = & 5x+\frac{8}{15} \\\Leftrightarrow & -24x-9& = & 5x+\frac{8}{15} \\ & & & \text{kgv van noemers 1 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(-24x-9)& = & (5x+\frac{8}{15}). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-135} & = & \color{red}{75x} +8 \\\Leftrightarrow & -360x \color{red}{-135} \color{blue}{+135} \color{blue}{-75x} & = & \color{red}{75x} +8 \color{blue}{-75x} \color{blue}{+135} \\\Leftrightarrow & -360x-75x& = & 8+135 \\\Leftrightarrow & \color{red}{-435} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-435} & & \\\Leftrightarrow & x = \frac{-143}{435} & & \\ & V = \left\{ \frac{-143}{435} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (3x-\frac{4}{11})& = & -2x+\frac{7}{15} \\\Leftrightarrow & 3x-\frac{4}{11}& = & -2x+\frac{7}{15} \\ & & & \text{kgv van noemers 11 en 15 is 165} \\\Leftrightarrow & \color{blue}{165} .(3x-\frac{4}{11})& = & (-2x+\frac{7}{15}). \color{blue}{165} \\\Leftrightarrow & 495x \color{red}{-60} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 495x \color{red}{-60} \color{blue}{+60} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+60} \\\Leftrightarrow & 495x+330x& = & 77+60 \\\Leftrightarrow & \color{red}{825} x& = & 137 \\\Leftrightarrow & x = \frac{137}{825} & & \\ & V = \left\{ \frac{137}{825} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (x+\frac{3}{7})& = & 9x+\frac{6}{13} \\\Leftrightarrow & 2x+\frac{6}{7}& = & 9x+\frac{6}{13} \\ & & & \text{kgv van noemers 7 en 13 is 91} \\\Leftrightarrow & \color{blue}{91} .(2x+\frac{6}{7})& = & (9x+\frac{6}{13}). \color{blue}{91} \\\Leftrightarrow & 182x \color{red}{+78} & = & \color{red}{819x} +42 \\\Leftrightarrow & 182x \color{red}{+78} \color{blue}{-78} \color{blue}{-819x} & = & \color{red}{819x} +42 \color{blue}{-819x} \color{blue}{-78} \\\Leftrightarrow & 182x-819x& = & 42-78 \\\Leftrightarrow & \color{red}{-637} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-637} & & \\\Leftrightarrow & x = \frac{36}{637} & & \\ & V = \left\{ \frac{36}{637} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (5x-\frac{4}{13})& = & -2x+\frac{7}{3} \\\Leftrightarrow & -5x+\frac{4}{13}& = & -2x+\frac{7}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(-5x+\frac{4}{13})& = & (-2x+\frac{7}{3}). \color{blue}{39} \\\Leftrightarrow & -195x \color{red}{+12} & = & \color{red}{-78x} +91 \\\Leftrightarrow & -195x \color{red}{+12} \color{blue}{-12} \color{blue}{+78x} & = & \color{red}{-78x} +91 \color{blue}{+78x} \color{blue}{-12} \\\Leftrightarrow & -195x+78x& = & 91-12 \\\Leftrightarrow & \color{red}{-117} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-117} & & \\\Leftrightarrow & x = \frac{-79}{117} & & \\ & V = \left\{ \frac{-79}{117} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{12})& = & x+\frac{6}{7} \\\Leftrightarrow & 30x-\frac{5}{2}& = & x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(30x-\frac{5}{2})& = & (x+\frac{6}{7}). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-35} & = & \color{red}{14x} +12 \\\Leftrightarrow & 420x \color{red}{-35} \color{blue}{+35} \color{blue}{-14x} & = & \color{red}{14x} +12 \color{blue}{-14x} \color{blue}{+35} \\\Leftrightarrow & 420x-14x& = & 12+35 \\\Leftrightarrow & \color{red}{406} x& = & 47 \\\Leftrightarrow & x = \frac{47}{406} & & \\ & V = \left\{ \frac{47}{406} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{15})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{16}{15}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 15 en 7 is 105} \\\Leftrightarrow & \color{blue}{105} .(12x+\frac{16}{15})& = & (7x+\frac{4}{7}). \color{blue}{105} \\\Leftrightarrow & 1260x \color{red}{+112} & = & \color{red}{735x} +60 \\\Leftrightarrow & 1260x \color{red}{+112} \color{blue}{-112} \color{blue}{-735x} & = & \color{red}{735x} +60 \color{blue}{-735x} \color{blue}{-112} \\\Leftrightarrow & 1260x-735x& = & 60-112 \\\Leftrightarrow & \color{red}{525} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{525} & & \\ & V = \left\{ \frac{-52}{525} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-03 12:56:51