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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{10}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & 378x+441x& = & 56-90 \\\Leftrightarrow & \color{red}{819} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{819} & & \\ & V = \left\{ \frac{-34}{819} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-12} \\\Leftrightarrow & 120x+45x& = & 10-12 \\\Leftrightarrow & \color{red}{165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{9})& = & 9x+\frac{7}{10} \\\Leftrightarrow & -8x+\frac{4}{9}& = & 9x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+40} & = & \color{red}{810x} +63 \\\Leftrightarrow & -720x \color{red}{+40} \color{blue}{-40} \color{blue}{-810x} & = & \color{red}{810x} +63 \color{blue}{-810x} \color{blue}{-40} \\\Leftrightarrow & -720x-810x& = & 63-40 \\\Leftrightarrow & \color{red}{-1530} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-1530} & & \\\Leftrightarrow & x = \frac{-23}{1530} & & \\ & V = \left\{ \frac{-23}{1530} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 24x+\frac{18}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x+ \frac{72}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{+72} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 672x \color{red}{+72} \color{blue}{-72} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{-72} \\\Leftrightarrow & 672x+140x& = & 21-72 \\\Leftrightarrow & \color{red}{812} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{812} & & \\ & V = \left\{ \frac{-51}{812} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+16} & = & \color{red}{-126x} +45 \\\Leftrightarrow & 144x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & 144x+126x& = & 45-16 \\\Leftrightarrow & \color{red}{270} x& = & 29 \\\Leftrightarrow & x = \frac{29}{270} & & \\ & V = \left\{ \frac{29}{270} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -10x-\frac{8}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-660}{ \color{blue}{66} }x- \frac{48}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{-462x} +77 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{+48} \\\Leftrightarrow & -660x+462x& = & 77+48 \\\Leftrightarrow & \color{red}{-198} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-198} & & \\\Leftrightarrow & x = \frac{-125}{198} & & \\ & V = \left\{ \frac{-125}{198} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+220} & = & \color{red}{231x} +18 \\\Leftrightarrow & -660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & -660x-231x& = & 18-220 \\\Leftrightarrow & \color{red}{-891} x& = & -202 \\\Leftrightarrow & x = \frac{-202}{-891} & & \\\Leftrightarrow & x = \frac{202}{891} & & \\ & V = \left\{ \frac{202}{891} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{8})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{25}{8}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x- \frac{75}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{-75} & = & \color{red}{-216x} +80 \\\Leftrightarrow & 240x \color{red}{-75} \color{blue}{+75} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{+75} \\\Leftrightarrow & 240x+216x& = & 80+75 \\\Leftrightarrow & \color{red}{456} x& = & 155 \\\Leftrightarrow & x = \frac{155}{456} & & \\ & V = \left\{ \frac{155}{456} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & -4x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -4x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+90} & = & \color{red}{-252x} +56 \\\Leftrightarrow & 945x \color{red}{+90} \color{blue}{-90} \color{blue}{+252x} & = & \color{red}{-252x} +56 \color{blue}{+252x} \color{blue}{-90} \\\Leftrightarrow & 945x+252x& = & 56-90 \\\Leftrightarrow & \color{red}{1197} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{1197} & & \\ & V = \left\{ \frac{-34}{1197} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{11})& = & 6x+\frac{3}{8} \\\Leftrightarrow & -18x+\frac{12}{11}& = & 6x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x+ \frac{96}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{+96} & = & \color{red}{528x} +33 \\\Leftrightarrow & -1584x \color{red}{+96} \color{blue}{-96} \color{blue}{-528x} & = & \color{red}{528x} +33 \color{blue}{-528x} \color{blue}{-96} \\\Leftrightarrow & -1584x-528x& = & 33-96 \\\Leftrightarrow & \color{red}{-2112} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-2112} & & \\\Leftrightarrow & x = \frac{21}{704} & & \\ & V = \left\{ \frac{21}{704} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 8x-\frac{10}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-90} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 504x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & 504x+441x& = & 70+90 \\\Leftrightarrow & \color{red}{945} x& = & 160 \\\Leftrightarrow & x = \frac{160}{945} & & \\\Leftrightarrow & x = \frac{32}{189} & & \\ & V = \left\{ \frac{32}{189} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{11})& = & 8x+\frac{7}{8} \\\Leftrightarrow & -15x-\frac{25}{11}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1320}{ \color{blue}{88} }x- \frac{200}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1320x \color{red}{-200} & = & \color{red}{704x} +77 \\\Leftrightarrow & -1320x \color{red}{-200} \color{blue}{+200} \color{blue}{-704x} & = & \color{red}{704x} +77 \color{blue}{-704x} \color{blue}{+200} \\\Leftrightarrow & -1320x-704x& = & 77+200 \\\Leftrightarrow & \color{red}{-2024} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-2024} & & \\\Leftrightarrow & x = \frac{-277}{2024} & & \\ & V = \left\{ \frac{-277}{2024} \right\} & \\\end{align}\)
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