Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-220} & = & \color{red}{539x} +49 \\\Leftrightarrow & 1155x \color{red}{-220} \color{blue}{+220} \color{blue}{-539x} & = & \color{red}{539x} +49 \color{blue}{-539x} \color{blue}{+220} \\\Leftrightarrow & 1155x-539x& = & 49+220 \\\Leftrightarrow & \color{red}{616} x& = & 269 \\\Leftrightarrow & x = \frac{269}{616} & & \\ & V = \left\{ \frac{269}{616} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{24}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+48} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+48} \color{blue}{-48} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-48} \\\Leftrightarrow & -120x-50x& = & 45-48 \\\Leftrightarrow & \color{red}{-170} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-170} & & \\\Leftrightarrow & x = \frac{3}{170} & & \\ & V = \left\{ \frac{3}{170} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{-54x} +7 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{+35} \\\Leftrightarrow & 84x+54x& = & 7+35 \\\Leftrightarrow & \color{red}{138} x& = & 42 \\\Leftrightarrow & x = \frac{42}{138} & & \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+72} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -180x+75x& = & 20-72 \\\Leftrightarrow & \color{red}{-105} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-105} & & \\\Leftrightarrow & x = \frac{52}{105} & & \\ & V = \left\{ \frac{52}{105} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-16} & = & \color{red}{63x} +3 \\\Leftrightarrow & -56x \color{red}{-16} \color{blue}{+16} \color{blue}{-63x} & = & \color{red}{63x} +3 \color{blue}{-63x} \color{blue}{+16} \\\Leftrightarrow & -56x-63x& = & 3+16 \\\Leftrightarrow & \color{red}{-119} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-119} & & \\\Leftrightarrow & x = \frac{-19}{119} & & \\ & V = \left\{ \frac{-19}{119} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-126} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -2310x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & -2310x+539x& = & 110+126 \\\Leftrightarrow & \color{red}{-1771} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1771} & & \\\Leftrightarrow & x = \frac{-236}{1771} & & \\ & V = \left\{ \frac{-236}{1771} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{11})& = & 9x+\frac{7}{12} \\\Leftrightarrow & -8x-\frac{8}{11}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1056}{ \color{blue}{132} }x- \frac{96}{ \color{blue}{132} })& = & (\frac{1188}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1056x \color{red}{-96} & = & \color{red}{1188x} +77 \\\Leftrightarrow & -1056x \color{red}{-96} \color{blue}{+96} \color{blue}{-1188x} & = & \color{red}{1188x} +77 \color{blue}{-1188x} \color{blue}{+96} \\\Leftrightarrow & -1056x-1188x& = & 77+96 \\\Leftrightarrow & \color{red}{-2244} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-2244} & & \\\Leftrightarrow & x = \frac{-173}{2244} & & \\ & V = \left\{ \frac{-173}{2244} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{11})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{28}{11}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-84} & = & \color{red}{99x} +44 \\\Leftrightarrow & -1155x \color{red}{-84} \color{blue}{+84} \color{blue}{-99x} & = & \color{red}{99x} +44 \color{blue}{-99x} \color{blue}{+84} \\\Leftrightarrow & -1155x-99x& = & 44+84 \\\Leftrightarrow & \color{red}{-1254} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-1254} & & \\\Leftrightarrow & x = \frac{-64}{627} & & \\ & V = \left\{ \frac{-64}{627} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 60x+25x& = & 8-12 \\\Leftrightarrow & \color{red}{85} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{85} & & \\ & V = \left\{ \frac{-4}{85} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{4})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 28x-\frac{35}{4}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{-315} & = & \color{red}{-324x} +32 \\\Leftrightarrow & 1008x \color{red}{-315} \color{blue}{+315} \color{blue}{+324x} & = & \color{red}{-324x} +32 \color{blue}{+324x} \color{blue}{+315} \\\Leftrightarrow & 1008x+324x& = & 32+315 \\\Leftrightarrow & \color{red}{1332} x& = & 347 \\\Leftrightarrow & x = \frac{347}{1332} & & \\ & V = \left\{ \frac{347}{1332} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -80x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -80x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{-115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-115} & & \\\Leftrightarrow & x = \frac{6}{115} & & \\ & V = \left\{ \frac{6}{115} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -16x-\frac{8}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-24} & = & \color{red}{105x} +40 \\\Leftrightarrow & -240x \color{red}{-24} \color{blue}{+24} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+24} \\\Leftrightarrow & -240x-105x& = & 40+24 \\\Leftrightarrow & \color{red}{-345} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-345} & & \\\Leftrightarrow & x = \frac{-64}{345} & & \\ & V = \left\{ \frac{-64}{345} \right\} & \\\end{align}\)
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