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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{9})& = & -2x+\frac{3}{4} \\\Leftrightarrow & -28x+\frac{14}{9}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1008}{ \color{blue}{36} }x+ \frac{56}{ \color{blue}{36} })& = & (\frac{-72}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{-72x} +27 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{+72x} & = & \color{red}{-72x} +27 \color{blue}{+72x} \color{blue}{-56} \\\Leftrightarrow & -1008x+72x& = & 27-56 \\\Leftrightarrow & \color{red}{-936} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-936} & & \\\Leftrightarrow & x = \frac{29}{936} & & \\ & V = \left\{ \frac{29}{936} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{11})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 21x+\frac{35}{11}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x+ \frac{70}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{+70} & = & \color{red}{-44x} +99 \\\Leftrightarrow & 462x \color{red}{+70} \color{blue}{-70} \color{blue}{+44x} & = & \color{red}{-44x} +99 \color{blue}{+44x} \color{blue}{-70} \\\Leftrightarrow & 462x+44x& = & 99-70 \\\Leftrightarrow & \color{red}{506} x& = & 29 \\\Leftrightarrow & x = \frac{29}{506} & & \\ & V = \left\{ \frac{29}{506} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{11})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{30}{11}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{+90} & = & \color{red}{-264x} +88 \\\Leftrightarrow & -594x \color{red}{+90} \color{blue}{-90} \color{blue}{+264x} & = & \color{red}{-264x} +88 \color{blue}{+264x} \color{blue}{-90} \\\Leftrightarrow & -594x+264x& = & 88-90 \\\Leftrightarrow & \color{red}{-330} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-330} & & \\\Leftrightarrow & x = \frac{1}{165} & & \\ & V = \left\{ \frac{1}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 14x+\frac{28}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{+140} & = & \color{red}{135x} +54 \\\Leftrightarrow & 630x \color{red}{+140} \color{blue}{-140} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-140} \\\Leftrightarrow & 630x-135x& = & 54-140 \\\Leftrightarrow & \color{red}{495} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{495} & & \\ & V = \left\{ \frac{-86}{495} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{6})& = & 4x+\frac{4}{7} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 4x+\frac{4}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{24}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{168x} +24 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{-168x} & = & \color{red}{168x} +24 \color{blue}{-168x} \color{blue}{+175} \\\Leftrightarrow & 630x-168x& = & 24+175 \\\Leftrightarrow & \color{red}{462} x& = & 199 \\\Leftrightarrow & x = \frac{199}{462} & & \\ & V = \left\{ \frac{199}{462} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 16x+\frac{8}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+40} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 880x \color{red}{+40} \color{blue}{-40} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-40} \\\Leftrightarrow & 880x+385x& = & 88-40 \\\Leftrightarrow & \color{red}{1265} x& = & 48 \\\Leftrightarrow & x = \frac{48}{1265} & & \\ & V = \left\{ \frac{48}{1265} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & 2x+\frac{5}{8} \\\Leftrightarrow & 21x+\frac{35}{2}& = & 2x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x+ \frac{140}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{+140} & = & \color{red}{16x} +5 \\\Leftrightarrow & 168x \color{red}{+140} \color{blue}{-140} \color{blue}{-16x} & = & \color{red}{16x} +5 \color{blue}{-16x} \color{blue}{-140} \\\Leftrightarrow & 168x-16x& = & 5-140 \\\Leftrightarrow & \color{red}{152} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{152} & & \\ & V = \left\{ \frac{-135}{152} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -324x \color{red}{+135} & = & \color{red}{-180x} +20 \\\Leftrightarrow & -324x \color{red}{+135} \color{blue}{-135} \color{blue}{+180x} & = & \color{red}{-180x} +20 \color{blue}{+180x} \color{blue}{-135} \\\Leftrightarrow & -324x+180x& = & 20-135 \\\Leftrightarrow & \color{red}{-144} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{-144} & & \\\Leftrightarrow & x = \frac{115}{144} & & \\ & V = \left\{ \frac{115}{144} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{+240} & = & \color{red}{280x} +63 \\\Leftrightarrow & -672x \color{red}{+240} \color{blue}{-240} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{-240} \\\Leftrightarrow & -672x-280x& = & 63-240 \\\Leftrightarrow & \color{red}{-952} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{-952} & & \\\Leftrightarrow & x = \frac{177}{952} & & \\ & V = \left\{ \frac{177}{952} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{15}{2}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{70x} +20 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{-70x} & = & \color{red}{70x} +20 \color{blue}{-70x} \color{blue}{+105} \\\Leftrightarrow & 168x-70x& = & 20+105 \\\Leftrightarrow & \color{red}{98} x& = & 125 \\\Leftrightarrow & x = \frac{125}{98} & & \\ & V = \left\{ \frac{125}{98} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+66} & = & \color{red}{231x} +56 \\\Leftrightarrow & -616x \color{red}{+66} \color{blue}{-66} \color{blue}{-231x} & = & \color{red}{231x} +56 \color{blue}{-231x} \color{blue}{-66} \\\Leftrightarrow & -616x-231x& = & 56-66 \\\Leftrightarrow & \color{red}{-847} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-847} & & \\\Leftrightarrow & x = \frac{10}{847} & & \\ & V = \left\{ \frac{10}{847} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & -90x+105x& = & 18-40 \\\Leftrightarrow & \color{red}{15} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{15} & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
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