Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{275x} +15 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 660x-275x& = & 15-132 \\\Leftrightarrow & \color{red}{385} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{385} & & \\ & V = \left\{ \frac{-117}{385} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+40} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 90x \color{red}{+40} \color{blue}{-40} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{-40} \\\Leftrightarrow & 90x+75x& = & 18-40 \\\Leftrightarrow & \color{red}{165} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{165} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & 6x+\frac{8}{3} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{54x} +24 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +24 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & -252x-54x& = & 24+28 \\\Leftrightarrow & \color{red}{-306} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-306} & & \\\Leftrightarrow & x = \frac{-26}{153} & & \\ & V = \left\{ \frac{-26}{153} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{7})& = & -4x+\frac{7}{10} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-280}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{+100} & = & \color{red}{-280x} +49 \\\Leftrightarrow & -1050x \color{red}{+100} \color{blue}{-100} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{-100} \\\Leftrightarrow & -1050x+280x& = & 49-100 \\\Leftrightarrow & \color{red}{-770} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-770} & & \\\Leftrightarrow & x = \frac{51}{770} & & \\ & V = \left\{ \frac{51}{770} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{18}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+54} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 450x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & 450x+105x& = & 10-54 \\\Leftrightarrow & \color{red}{555} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{555} & & \\ & V = \left\{ \frac{-44}{555} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -9x+\frac{5}{4} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{-32} & = & \color{red}{-108x} +15 \\\Leftrightarrow & 96x \color{red}{-32} \color{blue}{+32} \color{blue}{+108x} & = & \color{red}{-108x} +15 \color{blue}{+108x} \color{blue}{+32} \\\Leftrightarrow & 96x+108x& = & 15+32 \\\Leftrightarrow & \color{red}{204} x& = & 47 \\\Leftrightarrow & x = \frac{47}{204} & & \\ & V = \left\{ \frac{47}{204} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-200} & = & \color{red}{-350x} +49 \\\Leftrightarrow & -840x \color{red}{-200} \color{blue}{+200} \color{blue}{+350x} & = & \color{red}{-350x} +49 \color{blue}{+350x} \color{blue}{+200} \\\Leftrightarrow & -840x+350x& = & 49+200 \\\Leftrightarrow & \color{red}{-490} x& = & 249 \\\Leftrightarrow & x = \frac{249}{-490} & & \\\Leftrightarrow & x = \frac{-249}{490} & & \\ & V = \left\{ \frac{-249}{490} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x+ \frac{280}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{+280} & = & \color{red}{-216x} +21 \\\Leftrightarrow & -840x \color{red}{+280} \color{blue}{-280} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{-280} \\\Leftrightarrow & -840x+216x& = & 21-280 \\\Leftrightarrow & \color{red}{-624} x& = & -259 \\\Leftrightarrow & x = \frac{-259}{-624} & & \\\Leftrightarrow & x = \frac{259}{624} & & \\ & V = \left\{ \frac{259}{624} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -30x-\frac{12}{11}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{-48} & = & \color{red}{-308x} +77 \\\Leftrightarrow & -1320x \color{red}{-48} \color{blue}{+48} \color{blue}{+308x} & = & \color{red}{-308x} +77 \color{blue}{+308x} \color{blue}{+48} \\\Leftrightarrow & -1320x+308x& = & 77+48 \\\Leftrightarrow & \color{red}{-1012} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-1012} & & \\\Leftrightarrow & x = \frac{-125}{1012} & & \\ & V = \left\{ \frac{-125}{1012} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{6}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+66} & = & \color{red}{385x} +50 \\\Leftrightarrow & -550x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & -550x-385x& = & 50-66 \\\Leftrightarrow & \color{red}{-935} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-935} & & \\\Leftrightarrow & x = \frac{16}{935} & & \\ & V = \left\{ \frac{16}{935} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-162x} +45 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+162x} & = & \color{red}{-162x} +45 \color{blue}{+162x} \color{blue}{+16} \\\Leftrightarrow & -72x+162x& = & 45+16 \\\Leftrightarrow & \color{red}{90} x& = & 61 \\\Leftrightarrow & x = \frac{61}{90} & & \\ & V = \left\{ \frac{61}{90} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-168} \\\Leftrightarrow & -840x+245x& = & 10-168 \\\Leftrightarrow & \color{red}{-595} x& = & -158 \\\Leftrightarrow & x = \frac{-158}{-595} & & \\\Leftrightarrow & x = \frac{158}{595} & & \\ & V = \left\{ \frac{158}{595} \right\} & \\\end{align}\)
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