Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{-189x} +28 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+54} \\\Leftrightarrow & 504x+189x& = & 28+54 \\\Leftrightarrow & \color{red}{693} x& = & 82 \\\Leftrightarrow & x = \frac{82}{693} & & \\ & V = \left\{ \frac{82}{693} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{+147} & = & \color{red}{280x} +32 \\\Leftrightarrow & 784x \color{red}{+147} \color{blue}{-147} \color{blue}{-280x} & = & \color{red}{280x} +32 \color{blue}{-280x} \color{blue}{-147} \\\Leftrightarrow & 784x-280x& = & 32-147 \\\Leftrightarrow & \color{red}{504} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{504} & & \\ & V = \left\{ \frac{-115}{504} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{297x} +18 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 660x-297x& = & 18+220 \\\Leftrightarrow & \color{red}{363} x& = & 238 \\\Leftrightarrow & x = \frac{238}{363} & & \\ & V = \left\{ \frac{238}{363} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+88} & = & \color{red}{-165x} +18 \\\Leftrightarrow & 264x \color{red}{+88} \color{blue}{-88} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{-88} \\\Leftrightarrow & 264x+165x& = & 18-88 \\\Leftrightarrow & \color{red}{429} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{429} & & \\ & V = \left\{ \frac{-70}{429} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{5}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{-168x} +15 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{+98} \\\Leftrightarrow & -441x+168x& = & 15+98 \\\Leftrightarrow & \color{red}{-273} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-273} & & \\\Leftrightarrow & x = \frac{-113}{273} & & \\ & V = \left\{ \frac{-113}{273} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{18x} +21 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & -120x-18x& = & 21+40 \\\Leftrightarrow & \color{red}{-138} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-138} & & \\\Leftrightarrow & x = \frac{-61}{138} & & \\ & V = \left\{ \frac{-61}{138} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{+162} & = & \color{red}{-495x} +44 \\\Leftrightarrow & 2376x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & 2376x+495x& = & 44-162 \\\Leftrightarrow & \color{red}{2871} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{2871} & & \\ & V = \left\{ \frac{-118}{2871} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & 9x+\frac{8}{11} \\\Leftrightarrow & 4x+\frac{4}{7}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+44} & = & \color{red}{693x} +56 \\\Leftrightarrow & 308x \color{red}{+44} \color{blue}{-44} \color{blue}{-693x} & = & \color{red}{693x} +56 \color{blue}{-693x} \color{blue}{-44} \\\Leftrightarrow & 308x-693x& = & 56-44 \\\Leftrightarrow & \color{red}{-385} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-385} & & \\\Leftrightarrow & x = \frac{-12}{385} & & \\ & V = \left\{ \frac{-12}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{35x} +10 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & -84x-35x& = & 10-30 \\\Leftrightarrow & \color{red}{-119} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-119} & & \\\Leftrightarrow & x = \frac{20}{119} & & \\ & V = \left\{ \frac{20}{119} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{7})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+110} & = & \color{red}{693x} +35 \\\Leftrightarrow & 1925x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +35 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & 1925x-693x& = & 35-110 \\\Leftrightarrow & \color{red}{1232} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{1232} & & \\ & V = \left\{ \frac{-75}{1232} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{2})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{15}{2}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-75} & = & \color{red}{50x} +12 \\\Leftrightarrow & -90x \color{red}{-75} \color{blue}{+75} \color{blue}{-50x} & = & \color{red}{50x} +12 \color{blue}{-50x} \color{blue}{+75} \\\Leftrightarrow & -90x-50x& = & 12+75 \\\Leftrightarrow & \color{red}{-140} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-140} & & \\\Leftrightarrow & x = \frac{-87}{140} & & \\ & V = \left\{ \frac{-87}{140} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{2})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 12x-\frac{9}{2}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{45}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-45} & = & \color{red}{-50x} +18 \\\Leftrightarrow & 120x \color{red}{-45} \color{blue}{+45} \color{blue}{+50x} & = & \color{red}{-50x} +18 \color{blue}{+50x} \color{blue}{+45} \\\Leftrightarrow & 120x+50x& = & 18+45 \\\Leftrightarrow & \color{red}{170} x& = & 63 \\\Leftrightarrow & x = \frac{63}{170} & & \\ & V = \left\{ \frac{63}{170} \right\} & \\\end{align}\)
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