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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{+27} & = & \color{red}{60x} +80 \\\Leftrightarrow & 270x \color{red}{+27} \color{blue}{-27} \color{blue}{-60x} & = & \color{red}{60x} +80 \color{blue}{-60x} \color{blue}{-27} \\\Leftrightarrow & 270x-60x& = & 80-27 \\\Leftrightarrow & \color{red}{210} x& = & 53 \\\Leftrightarrow & x = \frac{53}{210} & & \\ & V = \left\{ \frac{53}{210} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{-18} & = & \color{red}{-77x} +4 \\\Leftrightarrow & 330x \color{red}{-18} \color{blue}{+18} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{+18} \\\Leftrightarrow & 330x+77x& = & 4+18 \\\Leftrightarrow & \color{red}{407} x& = & 22 \\\Leftrightarrow & x = \frac{22}{407} & & \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{+36} \\\Leftrightarrow & 120x+45x& = & 10+36 \\\Leftrightarrow & \color{red}{165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{165} & & \\ & V = \left\{ \frac{46}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{9})& = & 6x+\frac{10}{7} \\\Leftrightarrow & 25x+\frac{25}{9}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{+175} & = & \color{red}{378x} +90 \\\Leftrightarrow & 1575x \color{red}{+175} \color{blue}{-175} \color{blue}{-378x} & = & \color{red}{378x} +90 \color{blue}{-378x} \color{blue}{-175} \\\Leftrightarrow & 1575x-378x& = & 90-175 \\\Leftrightarrow & \color{red}{1197} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{1197} & & \\ & V = \left\{ \frac{-85}{1197} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{16x} +36 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-16x} & = & \color{red}{16x} +36 \color{blue}{-16x} \color{blue}{+21} \\\Leftrightarrow & 168x-16x& = & 36+21 \\\Leftrightarrow & \color{red}{152} x& = & 57 \\\Leftrightarrow & x = \frac{57}{152} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{-20} & = & \color{red}{21x} +2 \\\Leftrightarrow & -48x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & -48x-21x& = & 2+20 \\\Leftrightarrow & \color{red}{-69} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-69} & & \\\Leftrightarrow & x = \frac{-22}{69} & & \\ & V = \left\{ \frac{-22}{69} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-60} & = & \color{red}{-275x} +99 \\\Leftrightarrow & -495x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +99 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & -495x+275x& = & 99+60 \\\Leftrightarrow & \color{red}{-220} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-220} & & \\\Leftrightarrow & x = \frac{-159}{220} & & \\ & V = \left\{ \frac{-159}{220} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{+189} & = & \color{red}{-216x} +80 \\\Leftrightarrow & -1008x \color{red}{+189} \color{blue}{-189} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{-189} \\\Leftrightarrow & -1008x+216x& = & 80-189 \\\Leftrightarrow & \color{red}{-792} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-792} & & \\\Leftrightarrow & x = \frac{109}{792} & & \\ & V = \left\{ \frac{109}{792} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 16x-\frac{8}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{-24} & = & \color{red}{99x} +88 \\\Leftrightarrow & 528x \color{red}{-24} \color{blue}{+24} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+24} \\\Leftrightarrow & 528x-99x& = & 88+24 \\\Leftrightarrow & \color{red}{429} x& = & 112 \\\Leftrightarrow & x = \frac{112}{429} & & \\ & V = \left\{ \frac{112}{429} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{-180} & = & \color{red}{-550x} +99 \\\Leftrightarrow & -2640x \color{red}{-180} \color{blue}{+180} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{+180} \\\Leftrightarrow & -2640x+550x& = & 99+180 \\\Leftrightarrow & \color{red}{-2090} x& = & 279 \\\Leftrightarrow & x = \frac{279}{-2090} & & \\\Leftrightarrow & x = \frac{-279}{2090} & & \\ & V = \left\{ \frac{-279}{2090} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -15x+\frac{9}{5}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{160x} +45 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{-160x} & = & \color{red}{160x} +45 \color{blue}{-160x} \color{blue}{-36} \\\Leftrightarrow & -300x-160x& = & 45-36 \\\Leftrightarrow & \color{red}{-460} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-460} & & \\\Leftrightarrow & x = \frac{-9}{460} & & \\ & V = \left\{ \frac{-9}{460} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+40} & = & \color{red}{45x} +12 \\\Leftrightarrow & 150x \color{red}{+40} \color{blue}{-40} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-40} \\\Leftrightarrow & 150x-45x& = & 12-40 \\\Leftrightarrow & \color{red}{105} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{105} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
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