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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{504x} +49 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{-504x} & = & \color{red}{504x} +49 \color{blue}{-504x} \color{blue}{+80} \\\Leftrightarrow & 560x-504x& = & 49+80 \\\Leftrightarrow & \color{red}{56} x& = & 129 \\\Leftrightarrow & x = \frac{129}{56} & & \\ & V = \left\{ \frac{129}{56} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{11})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -25x+\frac{15}{11}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{+15} & = & \color{red}{-99x} +8 \\\Leftrightarrow & -275x \color{red}{+15} \color{blue}{-15} \color{blue}{+99x} & = & \color{red}{-99x} +8 \color{blue}{+99x} \color{blue}{-15} \\\Leftrightarrow & -275x+99x& = & 8-15 \\\Leftrightarrow & \color{red}{-176} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-176} & & \\\Leftrightarrow & x = \frac{7}{176} & & \\ & V = \left\{ \frac{7}{176} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{9})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-44} & = & \color{red}{297x} +72 \\\Leftrightarrow & 990x \color{red}{-44} \color{blue}{+44} \color{blue}{-297x} & = & \color{red}{297x} +72 \color{blue}{-297x} \color{blue}{+44} \\\Leftrightarrow & 990x-297x& = & 72+44 \\\Leftrightarrow & \color{red}{693} x& = & 116 \\\Leftrightarrow & x = \frac{116}{693} & & \\ & V = \left\{ \frac{116}{693} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+54} & = & \color{red}{-441x} +70 \\\Leftrightarrow & -378x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & -378x+441x& = & 70-54 \\\Leftrightarrow & \color{red}{63} x& = & 16 \\\Leftrightarrow & x = \frac{16}{63} & & \\ & V = \left\{ \frac{16}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{24}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+48} & = & \color{red}{110x} +33 \\\Leftrightarrow & 264x \color{red}{+48} \color{blue}{-48} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-48} \\\Leftrightarrow & 264x-110x& = & 33-48 \\\Leftrightarrow & \color{red}{154} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{154} & & \\ & V = \left\{ \frac{-15}{154} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-220} & = & \color{red}{385x} +42 \\\Leftrightarrow & -924x \color{red}{-220} \color{blue}{+220} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+220} \\\Leftrightarrow & -924x-385x& = & 42+220 \\\Leftrightarrow & \color{red}{-1309} x& = & 262 \\\Leftrightarrow & x = \frac{262}{-1309} & & \\\Leftrightarrow & x = \frac{-262}{1309} & & \\ & V = \left\{ \frac{-262}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 20+84 \\\Leftrightarrow & \color{red}{-245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-245} & & \\\Leftrightarrow & x = \frac{-104}{245} & & \\ & V = \left\{ \frac{-104}{245} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-99} & = & \color{red}{-275x} +35 \\\Leftrightarrow & 660x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +35 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & 660x+275x& = & 35+99 \\\Leftrightarrow & \color{red}{935} x& = & 134 \\\Leftrightarrow & x = \frac{134}{935} & & \\ & V = \left\{ \frac{134}{935} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & 9x+\frac{5}{7} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{189x} +15 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +15 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -168x-189x& = & 15-56 \\\Leftrightarrow & \color{red}{-357} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-357} & & \\\Leftrightarrow & x = \frac{41}{357} & & \\ & V = \left\{ \frac{41}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{6}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+6} & = & \color{red}{-77x} +2 \\\Leftrightarrow & -66x \color{red}{+6} \color{blue}{-6} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-6} \\\Leftrightarrow & -66x+77x& = & 2-6 \\\Leftrightarrow & \color{red}{11} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-24} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 264x \color{red}{-24} \color{blue}{+24} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{+24} \\\Leftrightarrow & 264x+154x& = & 33+24 \\\Leftrightarrow & \color{red}{418} x& = & 57 \\\Leftrightarrow & x = \frac{57}{418} & & \\\Leftrightarrow & x = \frac{3}{22} & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-616x} +40 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+616x} & = & \color{red}{-616x} +40 \color{blue}{+616x} \color{blue}{-165} \\\Leftrightarrow & 1320x+616x& = & 40-165 \\\Leftrightarrow & \color{red}{1936} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1936} & & \\ & V = \left\{ \frac{-125}{1936} \right\} & \\\end{align}\)
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