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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+20} & = & \color{red}{98x} +21 \\\Leftrightarrow & 84x \color{red}{+20} \color{blue}{-20} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{-20} \\\Leftrightarrow & 84x-98x& = & 21-20 \\\Leftrightarrow & \color{red}{-14} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-14} & & \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{45x} +6 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 54x-45x& = & 6+4 \\\Leftrightarrow & \color{red}{9} x& = & 10 \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{12}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{-24} & = & \color{red}{198x} +77 \\\Leftrightarrow & -440x \color{red}{-24} \color{blue}{+24} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{+24} \\\Leftrightarrow & -440x-198x& = & 77+24 \\\Leftrightarrow & \color{red}{-638} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-638} & & \\\Leftrightarrow & x = \frac{-101}{638} & & \\ & V = \left\{ \frac{-101}{638} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{385x} +15 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1650x-385x& = & 15+264 \\\Leftrightarrow & \color{red}{1265} x& = & 279 \\\Leftrightarrow & x = \frac{279}{1265} & & \\ & V = \left\{ \frac{279}{1265} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+100} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 180x \color{red}{+100} \color{blue}{-100} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{-100} \\\Leftrightarrow & 180x+75x& = & 18-100 \\\Leftrightarrow & \color{red}{255} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{255} & & \\ & V = \left\{ \frac{-82}{255} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{11})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-8} & = & \color{red}{-99x} +5 \\\Leftrightarrow & 88x \color{red}{-8} \color{blue}{+8} \color{blue}{+99x} & = & \color{red}{-99x} +5 \color{blue}{+99x} \color{blue}{+8} \\\Leftrightarrow & 88x+99x& = & 5+8 \\\Leftrightarrow & \color{red}{187} x& = & 13 \\\Leftrightarrow & x = \frac{13}{187} & & \\ & V = \left\{ \frac{13}{187} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1080}{ \color{blue}{60} }x+ \frac{288}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1080x \color{red}{+288} & = & \color{red}{300x} +25 \\\Leftrightarrow & 1080x \color{red}{+288} \color{blue}{-288} \color{blue}{-300x} & = & \color{red}{300x} +25 \color{blue}{-300x} \color{blue}{-288} \\\Leftrightarrow & 1080x-300x& = & 25-288 \\\Leftrightarrow & \color{red}{780} x& = & -263 \\\Leftrightarrow & x = \frac{-263}{780} & & \\ & V = \left\{ \frac{-263}{780} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-20} & = & \color{red}{21x} +4 \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & -30x-21x& = & 4+20 \\\Leftrightarrow & \color{red}{-51} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-51} & & \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+90} \\\Leftrightarrow & -594x+693x& = & 88+90 \\\Leftrightarrow & \color{red}{99} x& = & 178 \\\Leftrightarrow & x = \frac{178}{99} & & \\ & V = \left\{ \frac{178}{99} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-20} & = & \color{red}{112x} +49 \\\Leftrightarrow & -210x \color{red}{-20} \color{blue}{+20} \color{blue}{-112x} & = & \color{red}{112x} +49 \color{blue}{-112x} \color{blue}{+20} \\\Leftrightarrow & -210x-112x& = & 49+20 \\\Leftrightarrow & \color{red}{-322} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-322} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{11})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+32} & = & \color{red}{-396x} +33 \\\Leftrightarrow & -352x \color{red}{+32} \color{blue}{-32} \color{blue}{+396x} & = & \color{red}{-396x} +33 \color{blue}{+396x} \color{blue}{-32} \\\Leftrightarrow & -352x+396x& = & 33-32 \\\Leftrightarrow & \color{red}{44} x& = & 1 \\\Leftrightarrow & x = \frac{1}{44} & & \\ & V = \left\{ \frac{1}{44} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{11})& = & -6x+\frac{2}{5} \\\Leftrightarrow & -28x+\frac{28}{11}& = & -6x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x+ \frac{140}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{+140} & = & \color{red}{-330x} +22 \\\Leftrightarrow & -1540x \color{red}{+140} \color{blue}{-140} \color{blue}{+330x} & = & \color{red}{-330x} +22 \color{blue}{+330x} \color{blue}{-140} \\\Leftrightarrow & -1540x+330x& = & 22-140 \\\Leftrightarrow & \color{red}{-1210} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-1210} & & \\\Leftrightarrow & x = \frac{59}{605} & & \\ & V = \left\{ \frac{59}{605} \right\} & \\\end{align}\)
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