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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+18} & = & \color{red}{-189x} +70 \\\Leftrightarrow & -168x \color{red}{+18} \color{blue}{-18} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{-18} \\\Leftrightarrow & -168x+189x& = & 70-18 \\\Leftrightarrow & \color{red}{21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{+40} & = & \color{red}{-54x} +9 \\\Leftrightarrow & 96x \color{red}{+40} \color{blue}{-40} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-40} \\\Leftrightarrow & 96x+54x& = & 9-40 \\\Leftrightarrow & \color{red}{150} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{150} & & \\ & V = \left\{ \frac{-31}{150} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 18x-\frac{18}{5}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-198} & = & \color{red}{-275x} +35 \\\Leftrightarrow & 990x \color{red}{-198} \color{blue}{+198} \color{blue}{+275x} & = & \color{red}{-275x} +35 \color{blue}{+275x} \color{blue}{+198} \\\Leftrightarrow & 990x+275x& = & 35+198 \\\Leftrightarrow & \color{red}{1265} x& = & 233 \\\Leftrightarrow & x = \frac{233}{1265} & & \\ & V = \left\{ \frac{233}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{-15} & = & \color{red}{28x} +10 \\\Leftrightarrow & -40x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -40x-28x& = & 10+15 \\\Leftrightarrow & \color{red}{-68} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-68} & & \\\Leftrightarrow & x = \frac{-25}{68} & & \\ & V = \left\{ \frac{-25}{68} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{1}{2})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -14x+\frac{7}{2}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{+77} & = & \color{red}{110x} +14 \\\Leftrightarrow & -308x \color{red}{+77} \color{blue}{-77} \color{blue}{-110x} & = & \color{red}{110x} +14 \color{blue}{-110x} \color{blue}{-77} \\\Leftrightarrow & -308x-110x& = & 14-77 \\\Leftrightarrow & \color{red}{-418} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-418} & & \\\Leftrightarrow & x = \frac{63}{418} & & \\ & V = \left\{ \frac{63}{418} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{105x} +40 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 180x-105x& = & 40-36 \\\Leftrightarrow & \color{red}{75} x& = & 4 \\\Leftrightarrow & x = \frac{4}{75} & & \\ & V = \left\{ \frac{4}{75} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -9x-\frac{15}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-891}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -891x \color{red}{-135} & = & \color{red}{495x} +88 \\\Leftrightarrow & -891x \color{red}{-135} \color{blue}{+135} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+135} \\\Leftrightarrow & -891x-495x& = & 88+135 \\\Leftrightarrow & \color{red}{-1386} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-1386} & & \\\Leftrightarrow & x = \frac{-223}{1386} & & \\ & V = \left\{ \frac{-223}{1386} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{2})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{35}{2}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{56}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 56x \color{red}{-35} & = & \color{red}{-10x} +3 \\\Leftrightarrow & 56x \color{red}{-35} \color{blue}{+35} \color{blue}{+10x} & = & \color{red}{-10x} +3 \color{blue}{+10x} \color{blue}{+35} \\\Leftrightarrow & 56x+10x& = & 3+35 \\\Leftrightarrow & \color{red}{66} x& = & 38 \\\Leftrightarrow & x = \frac{38}{66} & & \\\Leftrightarrow & x = \frac{19}{33} & & \\ & V = \left\{ \frac{19}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{11})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+120} & = & \color{red}{-275x} +99 \\\Leftrightarrow & 660x \color{red}{+120} \color{blue}{-120} \color{blue}{+275x} & = & \color{red}{-275x} +99 \color{blue}{+275x} \color{blue}{-120} \\\Leftrightarrow & 660x+275x& = & 99-120 \\\Leftrightarrow & \color{red}{935} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{935} & & \\ & V = \left\{ \frac{-21}{935} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -4x+\frac{8}{9} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -4x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-135} & = & \color{red}{-396x} +88 \\\Leftrightarrow & -1485x \color{red}{-135} \color{blue}{+135} \color{blue}{+396x} & = & \color{red}{-396x} +88 \color{blue}{+396x} \color{blue}{+135} \\\Leftrightarrow & -1485x+396x& = & 88+135 \\\Leftrightarrow & \color{red}{-1089} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-1089} & & \\\Leftrightarrow & x = \frac{-223}{1089} & & \\ & V = \left\{ \frac{-223}{1089} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{3})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -15x-\frac{10}{3}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-135}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -135x \color{red}{-30} & = & \color{red}{72x} +4 \\\Leftrightarrow & -135x \color{red}{-30} \color{blue}{+30} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{+30} \\\Leftrightarrow & -135x-72x& = & 4+30 \\\Leftrightarrow & \color{red}{-207} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-207} & & \\\Leftrightarrow & x = \frac{-34}{207} & & \\ & V = \left\{ \frac{-34}{207} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +20 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 20-132 \\\Leftrightarrow & \color{red}{-385} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{-385} & & \\\Leftrightarrow & x = \frac{16}{55} & & \\ & V = \left\{ \frac{16}{55} \right\} & \\\end{align}\)
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