Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{3})& = & 2x+\frac{5}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 2x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{66x} +15 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +15 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 1155x-66x& = & 15+154 \\\Leftrightarrow & \color{red}{1089} x& = & 169 \\\Leftrightarrow & x = \frac{169}{1089} & & \\ & V = \left\{ \frac{169}{1089} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{25}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{-25} & = & \color{red}{77x} +2 \\\Leftrightarrow & -110x \color{red}{-25} \color{blue}{+25} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{+25} \\\Leftrightarrow & -110x-77x& = & 2+25 \\\Leftrightarrow & \color{red}{-187} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-187} & & \\\Leftrightarrow & x = \frac{-27}{187} & & \\ & V = \left\{ \frac{-27}{187} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{-60} & = & \color{red}{350x} +21 \\\Leftrightarrow & -630x \color{red}{-60} \color{blue}{+60} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{+60} \\\Leftrightarrow & -630x-350x& = & 21+60 \\\Leftrightarrow & \color{red}{-980} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-980} & & \\\Leftrightarrow & x = \frac{-81}{980} & & \\ & V = \left\{ \frac{-81}{980} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{24}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{120}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-120} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 630x \color{red}{-120} \color{blue}{+120} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+120} \\\Leftrightarrow & 630x+175x& = & 42+120 \\\Leftrightarrow & \color{red}{805} x& = & 162 \\\Leftrightarrow & x = \frac{162}{805} & & \\ & V = \left\{ \frac{162}{805} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-80} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 280x \color{red}{-80} \color{blue}{+80} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{+80} \\\Leftrightarrow & 280x+105x& = & 42+80 \\\Leftrightarrow & \color{red}{385} x& = & 122 \\\Leftrightarrow & x = \frac{122}{385} & & \\ & V = \left\{ \frac{122}{385} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+28} & = & \color{red}{18x} +5 \\\Leftrightarrow & -84x \color{red}{+28} \color{blue}{-28} \color{blue}{-18x} & = & \color{red}{18x} +5 \color{blue}{-18x} \color{blue}{-28} \\\Leftrightarrow & -84x-18x& = & 5-28 \\\Leftrightarrow & \color{red}{-102} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-102} & & \\\Leftrightarrow & x = \frac{23}{102} & & \\ & V = \left\{ \frac{23}{102} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 4x+\frac{7}{4} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 4x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{32x} +14 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{-32x} & = & \color{red}{32x} +14 \color{blue}{-32x} \color{blue}{+21} \\\Leftrightarrow & -280x-32x& = & 14+21 \\\Leftrightarrow & \color{red}{-312} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-312} & & \\\Leftrightarrow & x = \frac{-35}{312} & & \\ & V = \left\{ \frac{-35}{312} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{7}{9} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{405x} +35 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-405x} & = & \color{red}{405x} +35 \color{blue}{-405x} \color{blue}{+36} \\\Leftrightarrow & -180x-405x& = & 35+36 \\\Leftrightarrow & \color{red}{-585} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-585} & & \\\Leftrightarrow & x = \frac{-71}{585} & & \\ & V = \left\{ \frac{-71}{585} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{539x} +42 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -1540x-539x& = & 42-110 \\\Leftrightarrow & \color{red}{-2079} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-2079} & & \\\Leftrightarrow & x = \frac{68}{2079} & & \\ & V = \left\{ \frac{68}{2079} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & -1540x+539x& = & 42-110 \\\Leftrightarrow & \color{red}{-1001} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1001} & & \\\Leftrightarrow & x = \frac{68}{1001} & & \\ & V = \left\{ \frac{68}{1001} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{7})& = & -4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{25}{7}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+25} & = & \color{red}{-28x} +10 \\\Leftrightarrow & -105x \color{red}{+25} \color{blue}{-25} \color{blue}{+28x} & = & \color{red}{-28x} +10 \color{blue}{+28x} \color{blue}{-25} \\\Leftrightarrow & -105x+28x& = & 10-25 \\\Leftrightarrow & \color{red}{-77} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-77} & & \\\Leftrightarrow & x = \frac{15}{77} & & \\ & V = \left\{ \frac{15}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 990x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 990x-275x& = & 25+132 \\\Leftrightarrow & \color{red}{715} x& = & 157 \\\Leftrightarrow & x = \frac{157}{715} & & \\ & V = \left\{ \frac{157}{715} \right\} & \\\end{align}\)
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