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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x-\frac{4}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{36}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-36} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 378x \color{red}{-36} \color{blue}{+36} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+36} \\\Leftrightarrow & 378x+315x& = & 56+36 \\\Leftrightarrow & \color{red}{693} x& = & 92 \\\Leftrightarrow & x = \frac{92}{693} & & \\ & V = \left\{ \frac{92}{693} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{-16} & = & \color{red}{-126x} +15 \\\Leftrightarrow & -288x \color{red}{-16} \color{blue}{+16} \color{blue}{+126x} & = & \color{red}{-126x} +15 \color{blue}{+126x} \color{blue}{+16} \\\Leftrightarrow & -288x+126x& = & 15+16 \\\Leftrightarrow & \color{red}{-162} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-162} & & \\\Leftrightarrow & x = \frac{-31}{162} & & \\ & V = \left\{ \frac{-31}{162} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{7})& = & 2x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 2x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{-80} & = & \color{red}{56x} +63 \\\Leftrightarrow & -700x \color{red}{-80} \color{blue}{+80} \color{blue}{-56x} & = & \color{red}{56x} +63 \color{blue}{-56x} \color{blue}{+80} \\\Leftrightarrow & -700x-56x& = & 63+80 \\\Leftrightarrow & \color{red}{-756} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-756} & & \\\Leftrightarrow & x = \frac{-143}{756} & & \\ & V = \left\{ \frac{-143}{756} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{3})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{10}{3}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-70} & = & \color{red}{-105x} +30 \\\Leftrightarrow & 168x \color{red}{-70} \color{blue}{+70} \color{blue}{+105x} & = & \color{red}{-105x} +30 \color{blue}{+105x} \color{blue}{+70} \\\Leftrightarrow & 168x+105x& = & 30+70 \\\Leftrightarrow & \color{red}{273} x& = & 100 \\\Leftrightarrow & x = \frac{100}{273} & & \\ & V = \left\{ \frac{100}{273} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -20x-\frac{8}{3}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-88} & = & \color{red}{231x} +24 \\\Leftrightarrow & -660x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +24 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & -660x-231x& = & 24+88 \\\Leftrightarrow & \color{red}{-891} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-891} & & \\\Leftrightarrow & x = \frac{-112}{891} & & \\ & V = \left\{ \frac{-112}{891} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x+\frac{6}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+12} & = & \color{red}{154x} +77 \\\Leftrightarrow & -220x \color{red}{+12} \color{blue}{-12} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{-12} \\\Leftrightarrow & -220x-154x& = & 77-12 \\\Leftrightarrow & \color{red}{-374} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-374} & & \\\Leftrightarrow & x = \frac{-65}{374} & & \\ & V = \left\{ \frac{-65}{374} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{693x} +77 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{-693x} & = & \color{red}{693x} +77 \color{blue}{-693x} \color{blue}{-90} \\\Leftrightarrow & -990x-693x& = & 77-90 \\\Leftrightarrow & \color{red}{-1683} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-1683} & & \\\Leftrightarrow & x = \frac{13}{1683} & & \\ & V = \left\{ \frac{13}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{-315x} +45 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{+315x} & = & \color{red}{-315x} +45 \color{blue}{+315x} \color{blue}{-84} \\\Leftrightarrow & -280x+315x& = & 45-84 \\\Leftrightarrow & \color{red}{35} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{35} & & \\ & V = \left\{ \frac{-39}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{15}{8}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{+45} & = & \color{red}{-48x} +80 \\\Leftrightarrow & 216x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +80 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & 216x+48x& = & 80-45 \\\Leftrightarrow & \color{red}{264} x& = & 35 \\\Leftrightarrow & x = \frac{35}{264} & & \\ & V = \left\{ \frac{35}{264} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{245x} +50 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -210x-245x& = & 50-84 \\\Leftrightarrow & \color{red}{-455} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-455} & & \\\Leftrightarrow & x = \frac{34}{455} & & \\ & V = \left\{ \frac{34}{455} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-28} & = & \color{red}{-24x} +9 \\\Leftrightarrow & -168x \color{red}{-28} \color{blue}{+28} \color{blue}{+24x} & = & \color{red}{-24x} +9 \color{blue}{+24x} \color{blue}{+28} \\\Leftrightarrow & -168x+24x& = & 9+28 \\\Leftrightarrow & \color{red}{-144} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-144} & & \\\Leftrightarrow & x = \frac{-37}{144} & & \\ & V = \left\{ \frac{-37}{144} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-140} & = & \color{red}{441x} +45 \\\Leftrightarrow & 1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-441x} & = & \color{red}{441x} +45 \color{blue}{-441x} \color{blue}{+140} \\\Leftrightarrow & 1260x-441x& = & 45+140 \\\Leftrightarrow & \color{red}{819} x& = & 185 \\\Leftrightarrow & x = \frac{185}{819} & & \\ & V = \left\{ \frac{185}{819} \right\} & \\\end{align}\)
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