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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 126x+105x& = & 14-18 \\\Leftrightarrow & \color{red}{231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{231} & & \\ & V = \left\{ \frac{-4}{231} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{84x} +14 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-84x} & = & \color{red}{84x} +14 \color{blue}{-84x} \color{blue}{+30} \\\Leftrightarrow & -315x-84x& = & 14+30 \\\Leftrightarrow & \color{red}{-399} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-399} & & \\\Leftrightarrow & x = \frac{-44}{399} & & \\ & V = \left\{ \frac{-44}{399} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-20} & = & \color{red}{98x} +49 \\\Leftrightarrow & -280x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & -280x-98x& = & 49+20 \\\Leftrightarrow & \color{red}{-378} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-378} & & \\\Leftrightarrow & x = \frac{-23}{126} & & \\ & V = \left\{ \frac{-23}{126} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +44 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 44-54 \\\Leftrightarrow & \color{red}{-1221} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1221} & & \\\Leftrightarrow & x = \frac{10}{1221} & & \\ & V = \left\{ \frac{10}{1221} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 28x+\frac{28}{9}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x+ \frac{224}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{+224} & = & \color{red}{648x} +45 \\\Leftrightarrow & 2016x \color{red}{+224} \color{blue}{-224} \color{blue}{-648x} & = & \color{red}{648x} +45 \color{blue}{-648x} \color{blue}{-224} \\\Leftrightarrow & 2016x-648x& = & 45-224 \\\Leftrightarrow & \color{red}{1368} x& = & -179 \\\Leftrightarrow & x = \frac{-179}{1368} & & \\ & V = \left\{ \frac{-179}{1368} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{-63} & = & \color{red}{-168x} +16 \\\Leftrightarrow & -672x \color{red}{-63} \color{blue}{+63} \color{blue}{+168x} & = & \color{red}{-168x} +16 \color{blue}{+168x} \color{blue}{+63} \\\Leftrightarrow & -672x+168x& = & 16+63 \\\Leftrightarrow & \color{red}{-504} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-504} & & \\\Leftrightarrow & x = \frac{-79}{504} & & \\ & V = \left\{ \frac{-79}{504} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -8x+\frac{6}{5}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+54} & = & \color{red}{-135x} +25 \\\Leftrightarrow & -360x \color{red}{+54} \color{blue}{-54} \color{blue}{+135x} & = & \color{red}{-135x} +25 \color{blue}{+135x} \color{blue}{-54} \\\Leftrightarrow & -360x+135x& = & 25-54 \\\Leftrightarrow & \color{red}{-225} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-225} & & \\\Leftrightarrow & x = \frac{29}{225} & & \\ & V = \left\{ \frac{29}{225} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+54} & = & \color{red}{165x} +88 \\\Leftrightarrow & 792x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & 792x-165x& = & 88-54 \\\Leftrightarrow & \color{red}{627} x& = & 34 \\\Leftrightarrow & x = \frac{34}{627} & & \\ & V = \left\{ \frac{34}{627} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 72x+63x& = & 6+8 \\\Leftrightarrow & \color{red}{135} x& = & 14 \\\Leftrightarrow & x = \frac{14}{135} & & \\ & V = \left\{ \frac{14}{135} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{2})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{9}{2}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{+27} & = & \color{red}{12x} +20 \\\Leftrightarrow & 90x \color{red}{+27} \color{blue}{-27} \color{blue}{-12x} & = & \color{red}{12x} +20 \color{blue}{-12x} \color{blue}{-27} \\\Leftrightarrow & 90x-12x& = & 20-27 \\\Leftrightarrow & \color{red}{78} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{78} & & \\ & V = \left\{ \frac{-7}{78} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+84} & = & \color{red}{539x} +99 \\\Leftrightarrow & 924x \color{red}{+84} \color{blue}{-84} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-84} \\\Leftrightarrow & 924x-539x& = & 99-84 \\\Leftrightarrow & \color{red}{385} x& = & 15 \\\Leftrightarrow & x = \frac{15}{385} & & \\\Leftrightarrow & x = \frac{3}{77} & & \\ & V = \left\{ \frac{3}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+84} & = & \color{red}{105x} +20 \\\Leftrightarrow & 700x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 700x-105x& = & 20-84 \\\Leftrightarrow & \color{red}{595} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{595} & & \\ & V = \left\{ \frac{-64}{595} \right\} & \\\end{align}\)
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