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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{3})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+140} & = & \color{red}{105x} +24 \\\Leftrightarrow & 252x \color{red}{+140} \color{blue}{-140} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-140} \\\Leftrightarrow & 252x-105x& = & 24-140 \\\Leftrightarrow & \color{red}{147} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{147} & & \\ & V = \left\{ \frac{-116}{147} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{8})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{+105} & = & \color{red}{224x} +80 \\\Leftrightarrow & -840x \color{red}{+105} \color{blue}{-105} \color{blue}{-224x} & = & \color{red}{224x} +80 \color{blue}{-224x} \color{blue}{-105} \\\Leftrightarrow & -840x-224x& = & 80-105 \\\Leftrightarrow & \color{red}{-1064} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-1064} & & \\\Leftrightarrow & x = \frac{25}{1064} & & \\ & V = \left\{ \frac{25}{1064} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+54} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 594x \color{red}{+54} \color{blue}{-54} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-54} \\\Leftrightarrow & 594x+495x& = & 88-54 \\\Leftrightarrow & \color{red}{1089} x& = & 34 \\\Leftrightarrow & x = \frac{34}{1089} & & \\ & V = \left\{ \frac{34}{1089} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 8+12 \\\Leftrightarrow & \color{red}{-115} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-115} & & \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{6}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+42} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{+42} \color{blue}{-42} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-42} \\\Leftrightarrow & -924x-385x& = & 110-42 \\\Leftrightarrow & \color{red}{-1309} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-1309} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -4x+\frac{3}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -4x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{-60x} +9 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{-70} \\\Leftrightarrow & 315x+60x& = & 9-70 \\\Leftrightarrow & \color{red}{375} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{375} & & \\ & V = \left\{ \frac{-61}{375} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -9x+\frac{5}{7} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-56} & = & \color{red}{-189x} +15 \\\Leftrightarrow & -84x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +15 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & -84x+189x& = & 15+56 \\\Leftrightarrow & \color{red}{105} x& = & 71 \\\Leftrightarrow & x = \frac{71}{105} & & \\ & V = \left\{ \frac{71}{105} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{-300x} +25 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{-144} \\\Leftrightarrow & 720x+300x& = & 25-144 \\\Leftrightarrow & \color{red}{1020} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{1020} & & \\\Leftrightarrow & x = \frac{-7}{60} & & \\ & V = \left\{ \frac{-7}{60} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{8})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -21x-\frac{35}{8}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{315}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-315} & = & \color{red}{576x} +32 \\\Leftrightarrow & -1512x \color{red}{-315} \color{blue}{+315} \color{blue}{-576x} & = & \color{red}{576x} +32 \color{blue}{-576x} \color{blue}{+315} \\\Leftrightarrow & -1512x-576x& = & 32+315 \\\Leftrightarrow & \color{red}{-2088} x& = & 347 \\\Leftrightarrow & x = \frac{347}{-2088} & & \\\Leftrightarrow & x = \frac{-347}{2088} & & \\ & V = \left\{ \frac{-347}{2088} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{8})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 6x+\frac{15}{8}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+75} & = & \color{red}{-200x} +72 \\\Leftrightarrow & 240x \color{red}{+75} \color{blue}{-75} \color{blue}{+200x} & = & \color{red}{-200x} +72 \color{blue}{+200x} \color{blue}{-75} \\\Leftrightarrow & 240x+200x& = & 72-75 \\\Leftrightarrow & \color{red}{440} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{440} & & \\ & V = \left\{ \frac{-3}{440} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{+196} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 294x \color{red}{+196} \color{blue}{-196} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-196} \\\Leftrightarrow & 294x+63x& = & 30-196 \\\Leftrightarrow & \color{red}{357} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{357} & & \\ & V = \left\{ \frac{-166}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{5})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-36} & = & \color{red}{-30x} +50 \\\Leftrightarrow & 225x \color{red}{-36} \color{blue}{+36} \color{blue}{+30x} & = & \color{red}{-30x} +50 \color{blue}{+30x} \color{blue}{+36} \\\Leftrightarrow & 225x+30x& = & 50+36 \\\Leftrightarrow & \color{red}{255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{255} & & \\ & V = \left\{ \frac{86}{255} \right\} & \\\end{align}\)
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