Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{35}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+385} & = & \color{red}{297x} +18 \\\Leftrightarrow & -1155x \color{red}{+385} \color{blue}{-385} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{-385} \\\Leftrightarrow & -1155x-297x& = & 18-385 \\\Leftrightarrow & \color{red}{-1452} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-1452} & & \\\Leftrightarrow & x = \frac{367}{1452} & & \\ & V = \left\{ \frac{367}{1452} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-40} & = & \color{red}{140x} +35 \\\Leftrightarrow & 168x \color{red}{-40} \color{blue}{+40} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+40} \\\Leftrightarrow & 168x-140x& = & 35+40 \\\Leftrightarrow & \color{red}{28} x& = & 75 \\\Leftrightarrow & x = \frac{75}{28} & & \\ & V = \left\{ \frac{75}{28} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{18}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-126} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{-126} \color{blue}{+126} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+126} \\\Leftrightarrow & -420x-175x& = & 50+126 \\\Leftrightarrow & \color{red}{-595} x& = & 176 \\\Leftrightarrow & x = \frac{176}{-595} & & \\\Leftrightarrow & x = \frac{-176}{595} & & \\ & V = \left\{ \frac{-176}{595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 3x+\frac{5}{3} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+63} & = & \color{red}{72x} +40 \\\Leftrightarrow & 672x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +40 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & 672x-72x& = & 40-63 \\\Leftrightarrow & \color{red}{600} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{600} & & \\ & V = \left\{ \frac{-23}{600} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -20x+\frac{10}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+50} & = & \color{red}{105x} +12 \\\Leftrightarrow & -300x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -300x-105x& = & 12-50 \\\Leftrightarrow & \color{red}{-405} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-405} & & \\\Leftrightarrow & x = \frac{38}{405} & & \\ & V = \left\{ \frac{38}{405} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & -8x+\frac{3}{10} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{-200} & = & \color{red}{-560x} +21 \\\Leftrightarrow & 1050x \color{red}{-200} \color{blue}{+200} \color{blue}{+560x} & = & \color{red}{-560x} +21 \color{blue}{+560x} \color{blue}{+200} \\\Leftrightarrow & 1050x+560x& = & 21+200 \\\Leftrightarrow & \color{red}{1610} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1610} & & \\ & V = \left\{ \frac{221}{1610} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{72}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+72} & = & \color{red}{147x} +70 \\\Leftrightarrow & 504x \color{red}{+72} \color{blue}{-72} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-72} \\\Leftrightarrow & 504x-147x& = & 70-72 \\\Leftrightarrow & \color{red}{357} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{357} & & \\ & V = \left\{ \frac{-2}{357} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{-54x} +7 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{-28} \\\Leftrightarrow & 168x+54x& = & 7-28 \\\Leftrightarrow & \color{red}{222} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{222} & & \\\Leftrightarrow & x = \frac{-7}{74} & & \\ & V = \left\{ \frac{-7}{74} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-66} & = & \color{red}{220x} +50 \\\Leftrightarrow & -825x \color{red}{-66} \color{blue}{+66} \color{blue}{-220x} & = & \color{red}{220x} +50 \color{blue}{-220x} \color{blue}{+66} \\\Leftrightarrow & -825x-220x& = & 50+66 \\\Leftrightarrow & \color{red}{-1045} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-1045} & & \\\Leftrightarrow & x = \frac{-116}{1045} & & \\ & V = \left\{ \frac{-116}{1045} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1400}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1400x \color{red}{+160} & = & \color{red}{-490x} +63 \\\Leftrightarrow & 1400x \color{red}{+160} \color{blue}{-160} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{-160} \\\Leftrightarrow & 1400x+490x& = & 63-160 \\\Leftrightarrow & \color{red}{1890} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{1890} & & \\ & V = \left\{ \frac{-97}{1890} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 4x+\frac{7}{6} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 4x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{378}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 378x \color{red}{+36} & = & \color{red}{168x} +49 \\\Leftrightarrow & 378x \color{red}{+36} \color{blue}{-36} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{-36} \\\Leftrightarrow & 378x-168x& = & 49-36 \\\Leftrightarrow & \color{red}{210} x& = & 13 \\\Leftrightarrow & x = \frac{13}{210} & & \\ & V = \left\{ \frac{13}{210} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-45} & = & \color{red}{168x} +64 \\\Leftrightarrow & 360x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +64 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & 360x-168x& = & 64+45 \\\Leftrightarrow & \color{red}{192} x& = & 109 \\\Leftrightarrow & x = \frac{109}{192} & & \\ & V = \left\{ \frac{109}{192} \right\} & \\\end{align}\)
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