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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+132} & = & \color{red}{-495x} +25 \\\Leftrightarrow & -440x \color{red}{+132} \color{blue}{-132} \color{blue}{+495x} & = & \color{red}{-495x} +25 \color{blue}{+495x} \color{blue}{-132} \\\Leftrightarrow & -440x+495x& = & 25-132 \\\Leftrightarrow & \color{red}{55} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{55} & & \\ & V = \left\{ \frac{-107}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-20} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -140x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -140x+49x& = & 4+20 \\\Leftrightarrow & \color{red}{-91} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-91} & & \\\Leftrightarrow & x = \frac{-24}{91} & & \\ & V = \left\{ \frac{-24}{91} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{9})& = & 9x+\frac{5}{12} \\\Leftrightarrow & 28x+\frac{35}{9}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{+140} & = & \color{red}{324x} +15 \\\Leftrightarrow & 1008x \color{red}{+140} \color{blue}{-140} \color{blue}{-324x} & = & \color{red}{324x} +15 \color{blue}{-324x} \color{blue}{-140} \\\Leftrightarrow & 1008x-324x& = & 15-140 \\\Leftrightarrow & \color{red}{684} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{684} & & \\ & V = \left\{ \frac{-125}{684} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+18} & = & \color{red}{55x} +8 \\\Leftrightarrow & -132x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -132x-55x& = & 8-18 \\\Leftrightarrow & \color{red}{-187} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-187} & & \\\Leftrightarrow & x = \frac{10}{187} & & \\ & V = \left\{ \frac{10}{187} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-220} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 1540x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 1540x+231x& = & 42+220 \\\Leftrightarrow & \color{red}{1771} x& = & 262 \\\Leftrightarrow & x = \frac{262}{1771} & & \\ & V = \left\{ \frac{262}{1771} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{2})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -14x-\frac{7}{2}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{77}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-77} & = & \color{red}{66x} +16 \\\Leftrightarrow & -308x \color{red}{-77} \color{blue}{+77} \color{blue}{-66x} & = & \color{red}{66x} +16 \color{blue}{-66x} \color{blue}{+77} \\\Leftrightarrow & -308x-66x& = & 16+77 \\\Leftrightarrow & \color{red}{-374} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-374} & & \\\Leftrightarrow & x = \frac{-93}{374} & & \\ & V = \left\{ \frac{-93}{374} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & -4x+\frac{7}{6} \\\Leftrightarrow & -28x-\frac{28}{11}& = & -4x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1848}{ \color{blue}{66} }x- \frac{168}{ \color{blue}{66} })& = & (\frac{-264}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1848x \color{red}{-168} & = & \color{red}{-264x} +77 \\\Leftrightarrow & -1848x \color{red}{-168} \color{blue}{+168} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{+168} \\\Leftrightarrow & -1848x+264x& = & 77+168 \\\Leftrightarrow & \color{red}{-1584} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-1584} & & \\\Leftrightarrow & x = \frac{-245}{1584} & & \\ & V = \left\{ \frac{-245}{1584} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{4})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 108x \color{red}{-45} & = & \color{red}{24x} +16 \\\Leftrightarrow & 108x \color{red}{-45} \color{blue}{+45} \color{blue}{-24x} & = & \color{red}{24x} +16 \color{blue}{-24x} \color{blue}{+45} \\\Leftrightarrow & 108x-24x& = & 16+45 \\\Leftrightarrow & \color{red}{84} x& = & 61 \\\Leftrightarrow & x = \frac{61}{84} & & \\ & V = \left\{ \frac{61}{84} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{9})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{4}{9}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{720}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 720x \color{red}{+32} & = & \color{red}{-504x} +63 \\\Leftrightarrow & 720x \color{red}{+32} \color{blue}{-32} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{-32} \\\Leftrightarrow & 720x+504x& = & 63-32 \\\Leftrightarrow & \color{red}{1224} x& = & 31 \\\Leftrightarrow & x = \frac{31}{1224} & & \\ & V = \left\{ \frac{31}{1224} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{-72} & = & \color{red}{-210x} +25 \\\Leftrightarrow & 240x \color{red}{-72} \color{blue}{+72} \color{blue}{+210x} & = & \color{red}{-210x} +25 \color{blue}{+210x} \color{blue}{+72} \\\Leftrightarrow & 240x+210x& = & 25+72 \\\Leftrightarrow & \color{red}{450} x& = & 97 \\\Leftrightarrow & x = \frac{97}{450} & & \\ & V = \left\{ \frac{97}{450} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{5})& = & -9x+\frac{3}{11} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+132} & = & \color{red}{-495x} +15 \\\Leftrightarrow & -440x \color{red}{+132} \color{blue}{-132} \color{blue}{+495x} & = & \color{red}{-495x} +15 \color{blue}{+495x} \color{blue}{-132} \\\Leftrightarrow & -440x+495x& = & 15-132 \\\Leftrightarrow & \color{red}{55} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{55} & & \\ & V = \left\{ \frac{-117}{55} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{10}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-50} & = & \color{red}{495x} +66 \\\Leftrightarrow & -440x \color{red}{-50} \color{blue}{+50} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{+50} \\\Leftrightarrow & -440x-495x& = & 66+50 \\\Leftrightarrow & \color{red}{-935} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-935} & & \\\Leftrightarrow & x = \frac{-116}{935} & & \\ & V = \left\{ \frac{-116}{935} \right\} & \\\end{align}\)
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