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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 18x-\frac{24}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{-96} & = & \color{red}{308x} +99 \\\Leftrightarrow & 792x \color{red}{-96} \color{blue}{+96} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+96} \\\Leftrightarrow & 792x-308x& = & 99+96 \\\Leftrightarrow & \color{red}{484} x& = & 195 \\\Leftrightarrow & x = \frac{195}{484} & & \\ & V = \left\{ \frac{195}{484} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{12})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{25}{12}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{+25} & = & \color{red}{108x} +8 \\\Leftrightarrow & -240x \color{red}{+25} \color{blue}{-25} \color{blue}{-108x} & = & \color{red}{108x} +8 \color{blue}{-108x} \color{blue}{-25} \\\Leftrightarrow & -240x-108x& = & 8-25 \\\Leftrightarrow & \color{red}{-348} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-348} & & \\\Leftrightarrow & x = \frac{17}{348} & & \\ & V = \left\{ \frac{17}{348} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+10} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -70x+49x& = & 4-10 \\\Leftrightarrow & \color{red}{-21} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-21} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & -4x+\frac{5}{4} \\\Leftrightarrow & -28x+\frac{21}{11}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{84}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+84} & = & \color{red}{-176x} +55 \\\Leftrightarrow & -1232x \color{red}{+84} \color{blue}{-84} \color{blue}{+176x} & = & \color{red}{-176x} +55 \color{blue}{+176x} \color{blue}{-84} \\\Leftrightarrow & -1232x+176x& = & 55-84 \\\Leftrightarrow & \color{red}{-1056} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-1056} & & \\\Leftrightarrow & x = \frac{29}{1056} & & \\ & V = \left\{ \frac{29}{1056} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 450x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & 450x+105x& = & 50+36 \\\Leftrightarrow & \color{red}{555} x& = & 86 \\\Leftrightarrow & x = \frac{86}{555} & & \\ & V = \left\{ \frac{86}{555} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{7})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -21x-4& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x- \frac{44}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{-44} & = & \color{red}{88x} +10 \\\Leftrightarrow & -231x \color{red}{-44} \color{blue}{+44} \color{blue}{-88x} & = & \color{red}{88x} +10 \color{blue}{-88x} \color{blue}{+44} \\\Leftrightarrow & -231x-88x& = & 10+44 \\\Leftrightarrow & \color{red}{-319} x& = & 54 \\\Leftrightarrow & x = \frac{54}{-319} & & \\\Leftrightarrow & x = \frac{-54}{319} & & \\ & V = \left\{ \frac{-54}{319} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+20} & = & \color{red}{198x} +77 \\\Leftrightarrow & 176x \color{red}{+20} \color{blue}{-20} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{-20} \\\Leftrightarrow & 176x-198x& = & 77-20 \\\Leftrightarrow & \color{red}{-22} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-22} & & \\\Leftrightarrow & x = \frac{-57}{22} & & \\ & V = \left\{ \frac{-57}{22} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 12x-\frac{8}{9}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-8} & = & \color{red}{63x} +15 \\\Leftrightarrow & 108x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +15 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & 108x-63x& = & 15+8 \\\Leftrightarrow & \color{red}{45} x& = & 23 \\\Leftrightarrow & x = \frac{23}{45} & & \\ & V = \left\{ \frac{23}{45} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{147x} +14 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-90} \\\Leftrightarrow & -630x-147x& = & 14-90 \\\Leftrightarrow & \color{red}{-777} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-777} & & \\\Leftrightarrow & x = \frac{76}{777} & & \\ & V = \left\{ \frac{76}{777} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{11})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{15}{11}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{+30} & = & \color{red}{66x} +99 \\\Leftrightarrow & -440x \color{red}{+30} \color{blue}{-30} \color{blue}{-66x} & = & \color{red}{66x} +99 \color{blue}{-66x} \color{blue}{-30} \\\Leftrightarrow & -440x-66x& = & 99-30 \\\Leftrightarrow & \color{red}{-506} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-506} & & \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 28x+\frac{14}{9}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x+ \frac{112}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{+112} & = & \color{red}{-216x} +27 \\\Leftrightarrow & 2016x \color{red}{+112} \color{blue}{-112} \color{blue}{+216x} & = & \color{red}{-216x} +27 \color{blue}{+216x} \color{blue}{-112} \\\Leftrightarrow & 2016x+216x& = & 27-112 \\\Leftrightarrow & \color{red}{2232} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{2232} & & \\ & V = \left\{ \frac{-85}{2232} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 70-66 \\\Leftrightarrow & \color{red}{77} x& = & 4 \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
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