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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -90x+105x& = & 50-18 \\\Leftrightarrow & \color{red}{15} x& = & 32 \\\Leftrightarrow & x = \frac{32}{15} & & \\ & V = \left\{ \frac{32}{15} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -180x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -180x+50x& = & 15+24 \\\Leftrightarrow & \color{red}{-130} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-130} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{18}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+54} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & -180x-75x& = & 50-54 \\\Leftrightarrow & \color{red}{-255} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-255} & & \\\Leftrightarrow & x = \frac{4}{255} & & \\ & V = \left\{ \frac{4}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{8})& = & -8x+\frac{9}{4} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-15} & = & \color{red}{-64x} +18 \\\Leftrightarrow & -120x \color{red}{-15} \color{blue}{+15} \color{blue}{+64x} & = & \color{red}{-64x} +18 \color{blue}{+64x} \color{blue}{+15} \\\Leftrightarrow & -120x+64x& = & 18+15 \\\Leftrightarrow & \color{red}{-56} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-56} & & \\\Leftrightarrow & x = \frac{-33}{56} & & \\ & V = \left\{ \frac{-33}{56} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -8x+\frac{5}{3} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -8x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{-168x} +35 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{+168x} & = & \color{red}{-168x} +35 \color{blue}{+168x} \color{blue}{+30} \\\Leftrightarrow & -315x+168x& = & 35+30 \\\Leftrightarrow & \color{red}{-147} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-147} & & \\\Leftrightarrow & x = \frac{-65}{147} & & \\ & V = \left\{ \frac{-65}{147} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-10} & = & \color{red}{-49x} +6 \\\Leftrightarrow & 42x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & 42x+49x& = & 6+10 \\\Leftrightarrow & \color{red}{91} x& = & 16 \\\Leftrightarrow & x = \frac{16}{91} & & \\ & V = \left\{ \frac{16}{91} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & -5x+\frac{3}{8} \\\Leftrightarrow & -12x-\frac{24}{11}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{192}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-192} & = & \color{red}{-440x} +33 \\\Leftrightarrow & -1056x \color{red}{-192} \color{blue}{+192} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{+192} \\\Leftrightarrow & -1056x+440x& = & 33+192 \\\Leftrightarrow & \color{red}{-616} x& = & 225 \\\Leftrightarrow & x = \frac{225}{-616} & & \\\Leftrightarrow & x = \frac{-225}{616} & & \\ & V = \left\{ \frac{-225}{616} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{6}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+30} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -550x \color{red}{+30} \color{blue}{-30} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-30} \\\Leftrightarrow & -550x+385x& = & 66-30 \\\Leftrightarrow & \color{red}{-165} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-165} & & \\\Leftrightarrow & x = \frac{-12}{55} & & \\ & V = \left\{ \frac{-12}{55} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{11})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -25x-\frac{10}{11}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{-90} & = & \color{red}{891x} +88 \\\Leftrightarrow & -2475x \color{red}{-90} \color{blue}{+90} \color{blue}{-891x} & = & \color{red}{891x} +88 \color{blue}{-891x} \color{blue}{+90} \\\Leftrightarrow & -2475x-891x& = & 88+90 \\\Leftrightarrow & \color{red}{-3366} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-3366} & & \\\Leftrightarrow & x = \frac{-89}{1683} & & \\ & V = \left\{ \frac{-89}{1683} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{-32} & = & \color{red}{-60x} +21 \\\Leftrightarrow & 48x \color{red}{-32} \color{blue}{+32} \color{blue}{+60x} & = & \color{red}{-60x} +21 \color{blue}{+60x} \color{blue}{+32} \\\Leftrightarrow & 48x+60x& = & 21+32 \\\Leftrightarrow & \color{red}{108} x& = & 53 \\\Leftrightarrow & x = \frac{53}{108} & & \\ & V = \left\{ \frac{53}{108} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{9})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x+\frac{10}{9}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+50} & = & \color{red}{315x} +36 \\\Leftrightarrow & -270x \color{red}{+50} \color{blue}{-50} \color{blue}{-315x} & = & \color{red}{315x} +36 \color{blue}{-315x} \color{blue}{-50} \\\Leftrightarrow & -270x-315x& = & 36-50 \\\Leftrightarrow & \color{red}{-585} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-585} & & \\\Leftrightarrow & x = \frac{14}{585} & & \\ & V = \left\{ \frac{14}{585} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{11})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{-10} & = & \color{red}{77x} +7 \\\Leftrightarrow & 44x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +7 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & 44x-77x& = & 7+10 \\\Leftrightarrow & \color{red}{-33} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-33} & & \\\Leftrightarrow & x = \frac{-17}{33} & & \\ & V = \left\{ \frac{-17}{33} \right\} & \\\end{align}\)
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