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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-189} & = & \color{red}{216x} +64 \\\Leftrightarrow & -1008x \color{red}{-189} \color{blue}{+189} \color{blue}{-216x} & = & \color{red}{216x} +64 \color{blue}{-216x} \color{blue}{+189} \\\Leftrightarrow & -1008x-216x& = & 64+189 \\\Leftrightarrow & \color{red}{-1224} x& = & 253 \\\Leftrightarrow & x = \frac{253}{-1224} & & \\\Leftrightarrow & x = \frac{-253}{1224} & & \\ & V = \left\{ \frac{-253}{1224} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{11})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -8x+\frac{10}{11}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+50} & = & \color{red}{495x} +22 \\\Leftrightarrow & -440x \color{red}{+50} \color{blue}{-50} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{-50} \\\Leftrightarrow & -440x-495x& = & 22-50 \\\Leftrightarrow & \color{red}{-935} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-935} & & \\\Leftrightarrow & x = \frac{28}{935} & & \\ & V = \left\{ \frac{28}{935} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{-60x} +9 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{-56} \\\Leftrightarrow & 252x+60x& = & 9-56 \\\Leftrightarrow & \color{red}{312} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{312} & & \\ & V = \left\{ \frac{-47}{312} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & -9x+\frac{2}{7} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+10} & = & \color{red}{-63x} +2 \\\Leftrightarrow & 140x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & 140x+63x& = & 2-10 \\\Leftrightarrow & \color{red}{203} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{203} & & \\ & V = \left\{ \frac{-8}{203} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+6} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 70x \color{red}{+6} \color{blue}{-6} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{-6} \\\Leftrightarrow & 70x+21x& = & 3-6 \\\Leftrightarrow & \color{red}{91} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{91} & & \\ & V = \left\{ \frac{-3}{91} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{147x} +49 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{-147x} & = & \color{red}{147x} +49 \color{blue}{-147x} \color{blue}{+90} \\\Leftrightarrow & 630x-147x& = & 49+90 \\\Leftrightarrow & \color{red}{483} x& = & 139 \\\Leftrightarrow & x = \frac{139}{483} & & \\ & V = \left\{ \frac{139}{483} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+36} & = & \color{red}{110x} +77 \\\Leftrightarrow & 264x \color{red}{+36} \color{blue}{-36} \color{blue}{-110x} & = & \color{red}{110x} +77 \color{blue}{-110x} \color{blue}{-36} \\\Leftrightarrow & 264x-110x& = & 77-36 \\\Leftrightarrow & \color{red}{154} x& = & 41 \\\Leftrightarrow & x = \frac{41}{154} & & \\ & V = \left\{ \frac{41}{154} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{4}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-28} & = & \color{red}{245x} +45 \\\Leftrightarrow & -350x \color{red}{-28} \color{blue}{+28} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+28} \\\Leftrightarrow & -350x-245x& = & 45+28 \\\Leftrightarrow & \color{red}{-595} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-595} & & \\\Leftrightarrow & x = \frac{-73}{595} & & \\ & V = \left\{ \frac{-73}{595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{-120x} +48 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{+120x} & = & \color{red}{-120x} +48 \color{blue}{+120x} \color{blue}{+105} \\\Leftrightarrow & -560x+120x& = & 48+105 \\\Leftrightarrow & \color{red}{-440} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-440} & & \\\Leftrightarrow & x = \frac{-153}{440} & & \\ & V = \left\{ \frac{-153}{440} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x+ \frac{240}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{+240} & = & \color{red}{-616x} +55 \\\Leftrightarrow & -2640x \color{red}{+240} \color{blue}{-240} \color{blue}{+616x} & = & \color{red}{-616x} +55 \color{blue}{+616x} \color{blue}{-240} \\\Leftrightarrow & -2640x+616x& = & 55-240 \\\Leftrightarrow & \color{red}{-2024} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-2024} & & \\\Leftrightarrow & x = \frac{185}{2024} & & \\ & V = \left\{ \frac{185}{2024} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{25}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+25} & = & \color{red}{-27x} +10 \\\Leftrightarrow & -180x \color{red}{+25} \color{blue}{-25} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{-25} \\\Leftrightarrow & -180x+27x& = & 10-25 \\\Leftrightarrow & \color{red}{-153} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-153} & & \\\Leftrightarrow & x = \frac{5}{51} & & \\ & V = \left\{ \frac{5}{51} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{4})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 12x-\frac{9}{4}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x- \frac{99}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{-99} & = & \color{red}{220x} +36 \\\Leftrightarrow & 528x \color{red}{-99} \color{blue}{+99} \color{blue}{-220x} & = & \color{red}{220x} +36 \color{blue}{-220x} \color{blue}{+99} \\\Leftrightarrow & 528x-220x& = & 36+99 \\\Leftrightarrow & \color{red}{308} x& = & 135 \\\Leftrightarrow & x = \frac{135}{308} & & \\ & V = \left\{ \frac{135}{308} \right\} & \\\end{align}\)
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