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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{-50x} +9 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{-36} \\\Leftrightarrow & 240x+50x& = & 9-36 \\\Leftrightarrow & \color{red}{290} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{290} & & \\ & V = \left\{ \frac{-27}{290} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{15}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+75} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1100x \color{red}{+75} \color{blue}{-75} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-75} \\\Leftrightarrow & -1100x+385x& = & 66-75 \\\Leftrightarrow & \color{red}{-715} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-715} & & \\\Leftrightarrow & x = \frac{9}{715} & & \\ & V = \left\{ \frac{9}{715} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{7})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-80} & = & \color{red}{-196x} +49 \\\Leftrightarrow & 280x \color{red}{-80} \color{blue}{+80} \color{blue}{+196x} & = & \color{red}{-196x} +49 \color{blue}{+196x} \color{blue}{+80} \\\Leftrightarrow & 280x+196x& = & 49+80 \\\Leftrightarrow & \color{red}{476} x& = & 129 \\\Leftrightarrow & x = \frac{129}{476} & & \\ & V = \left\{ \frac{129}{476} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -20x+\frac{8}{9}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{45}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{+32} & = & \color{red}{252x} +45 \\\Leftrightarrow & -720x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +45 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -720x-252x& = & 45-32 \\\Leftrightarrow & \color{red}{-972} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-972} & & \\\Leftrightarrow & x = \frac{-13}{972} & & \\ & V = \left\{ \frac{-13}{972} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{3})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -14x-\frac{28}{3}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{84}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-84} & = & \color{red}{-27x} +2 \\\Leftrightarrow & -126x \color{red}{-84} \color{blue}{+84} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+84} \\\Leftrightarrow & -126x+27x& = & 2+84 \\\Leftrightarrow & \color{red}{-99} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-99} & & \\\Leftrightarrow & x = \frac{-86}{99} & & \\ & V = \left\{ \frac{-86}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+8} & = & \color{red}{-90x} +7 \\\Leftrightarrow & 100x \color{red}{+8} \color{blue}{-8} \color{blue}{+90x} & = & \color{red}{-90x} +7 \color{blue}{+90x} \color{blue}{-8} \\\Leftrightarrow & 100x+90x& = & 7-8 \\\Leftrightarrow & \color{red}{190} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{190} & & \\ & V = \left\{ \frac{-1}{190} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+1)& = & -5x+\frac{9}{2} \\\Leftrightarrow & 14x-7& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x- \frac{14}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{-14} & = & \color{red}{-10x} +9 \\\Leftrightarrow & 28x \color{red}{-14} \color{blue}{+14} \color{blue}{+10x} & = & \color{red}{-10x} +9 \color{blue}{+10x} \color{blue}{+14} \\\Leftrightarrow & 28x+10x& = & 9+14 \\\Leftrightarrow & \color{red}{38} x& = & 23 \\\Leftrightarrow & x = \frac{23}{38} & & \\ & V = \left\{ \frac{23}{38} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{8}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+8} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -40x \color{red}{+8} \color{blue}{-8} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-8} \\\Leftrightarrow & -40x+45x& = & 6-8 \\\Leftrightarrow & \color{red}{5} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{16}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{-32} & = & \color{red}{198x} +99 \\\Leftrightarrow & -176x \color{red}{-32} \color{blue}{+32} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{+32} \\\Leftrightarrow & -176x-198x& = & 99+32 \\\Leftrightarrow & \color{red}{-374} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-374} & & \\\Leftrightarrow & x = \frac{-131}{374} & & \\ & V = \left\{ \frac{-131}{374} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+98} & = & \color{red}{168x} +30 \\\Leftrightarrow & -441x \color{red}{+98} \color{blue}{-98} \color{blue}{-168x} & = & \color{red}{168x} +30 \color{blue}{-168x} \color{blue}{-98} \\\Leftrightarrow & -441x-168x& = & 30-98 \\\Leftrightarrow & \color{red}{-609} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-609} & & \\\Leftrightarrow & x = \frac{68}{609} & & \\ & V = \left\{ \frac{68}{609} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+6} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -45x \color{red}{+6} \color{blue}{-6} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-6} \\\Leftrightarrow & -45x+25x& = & 6-6 \\\Leftrightarrow & \color{red}{-20} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-20} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -24x+\frac{24}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+264} & = & \color{red}{-385x} +56 \\\Leftrightarrow & -1848x \color{red}{+264} \color{blue}{-264} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-264} \\\Leftrightarrow & -1848x+385x& = & 56-264 \\\Leftrightarrow & \color{red}{-1463} x& = & -208 \\\Leftrightarrow & x = \frac{-208}{-1463} & & \\\Leftrightarrow & x = \frac{208}{1463} & & \\ & V = \left\{ \frac{208}{1463} \right\} & \\\end{align}\)
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