Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{4}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{20}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-20} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 280x \color{red}{-20} \color{blue}{+20} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{+20} \\\Leftrightarrow & 280x+105x& = & 42+20 \\\Leftrightarrow & \color{red}{385} x& = & 62 \\\Leftrightarrow & x = \frac{62}{385} & & \\ & V = \left\{ \frac{62}{385} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{11})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -18x-\frac{30}{11}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{297x} +110 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{+90} \\\Leftrightarrow & -594x-297x& = & 110+90 \\\Leftrightarrow & \color{red}{-891} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-891} & & \\\Leftrightarrow & x = \frac{-200}{891} & & \\ & V = \left\{ \frac{-200}{891} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{24}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-48} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & -120x-50x& = & 45+48 \\\Leftrightarrow & \color{red}{-170} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-170} & & \\\Leftrightarrow & x = \frac{-93}{170} & & \\ & V = \left\{ \frac{-93}{170} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-30} & = & \color{red}{-70x} +42 \\\Leftrightarrow & 525x \color{red}{-30} \color{blue}{+30} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{+30} \\\Leftrightarrow & 525x+70x& = & 42+30 \\\Leftrightarrow & \color{red}{595} x& = & 72 \\\Leftrightarrow & x = \frac{72}{595} & & \\ & V = \left\{ \frac{72}{595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-96} & = & \color{red}{100x} +35 \\\Leftrightarrow & 240x \color{red}{-96} \color{blue}{+96} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{+96} \\\Leftrightarrow & 240x-100x& = & 35+96 \\\Leftrightarrow & \color{red}{140} x& = & 131 \\\Leftrightarrow & x = \frac{131}{140} & & \\ & V = \left\{ \frac{131}{140} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{6}{5}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-50}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -50x \color{red}{+6} & = & \color{red}{35x} +8 \\\Leftrightarrow & -50x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & -50x-35x& = & 8-6 \\\Leftrightarrow & \color{red}{-85} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-85} & & \\\Leftrightarrow & x = \frac{-2}{85} & & \\ & V = \left\{ \frac{-2}{85} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{4}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+12} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -330x \color{red}{+12} \color{blue}{-12} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-12} \\\Leftrightarrow & -330x+231x& = & 44-12 \\\Leftrightarrow & \color{red}{-99} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-99} & & \\\Leftrightarrow & x = \frac{-32}{99} & & \\ & V = \left\{ \frac{-32}{99} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1680x \color{red}{-192} & = & \color{red}{588x} +35 \\\Leftrightarrow & 1680x \color{red}{-192} \color{blue}{+192} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{+192} \\\Leftrightarrow & 1680x-588x& = & 35+192 \\\Leftrightarrow & \color{red}{1092} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1092} & & \\ & V = \left\{ \frac{227}{1092} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-100} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-100} \color{blue}{+100} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+100} \\\Leftrightarrow & 420x-175x& = & 42+100 \\\Leftrightarrow & \color{red}{245} x& = & 142 \\\Leftrightarrow & x = \frac{142}{245} & & \\ & V = \left\{ \frac{142}{245} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{297x} +30 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +30 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & -1155x-297x& = & 30-154 \\\Leftrightarrow & \color{red}{-1452} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{-1452} & & \\\Leftrightarrow & x = \frac{31}{363} & & \\ & V = \left\{ \frac{31}{363} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{30x} +10 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{+36} \\\Leftrightarrow & 135x-30x& = & 10+36 \\\Leftrightarrow & \color{red}{105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{105} & & \\ & V = \left\{ \frac{46}{105} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{5})& = & 8x+\frac{9}{11} \\\Leftrightarrow & 21x+\frac{21}{5}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x+ \frac{231}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{+231} & = & \color{red}{440x} +45 \\\Leftrightarrow & 1155x \color{red}{+231} \color{blue}{-231} \color{blue}{-440x} & = & \color{red}{440x} +45 \color{blue}{-440x} \color{blue}{-231} \\\Leftrightarrow & 1155x-440x& = & 45-231 \\\Leftrightarrow & \color{red}{715} x& = & -186 \\\Leftrightarrow & x = \frac{-186}{715} & & \\ & V = \left\{ \frac{-186}{715} \right\} & \\\end{align}\)
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