Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{7})& = & 9x+\frac{5}{3} \\\Leftrightarrow & -8x-\frac{8}{7}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-24} & = & \color{red}{189x} +35 \\\Leftrightarrow & -168x \color{red}{-24} \color{blue}{+24} \color{blue}{-189x} & = & \color{red}{189x} +35 \color{blue}{-189x} \color{blue}{+24} \\\Leftrightarrow & -168x-189x& = & 35+24 \\\Leftrightarrow & \color{red}{-357} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-357} & & \\\Leftrightarrow & x = \frac{-59}{357} & & \\ & V = \left\{ \frac{-59}{357} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 15x+\frac{9}{10}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+63} & = & \color{red}{-490x} +60 \\\Leftrightarrow & 1050x \color{red}{+63} \color{blue}{-63} \color{blue}{+490x} & = & \color{red}{-490x} +60 \color{blue}{+490x} \color{blue}{-63} \\\Leftrightarrow & 1050x+490x& = & 60-63 \\\Leftrightarrow & \color{red}{1540} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{1540} & & \\ & V = \left\{ \frac{-3}{1540} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 3x+\frac{8}{5} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+50} & = & \color{red}{105x} +56 \\\Leftrightarrow & -700x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -700x-105x& = & 56-50 \\\Leftrightarrow & \color{red}{-805} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-805} & & \\\Leftrightarrow & x = \frac{-6}{805} & & \\ & V = \left\{ \frac{-6}{805} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{4})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{25}{4}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{+125} & = & \color{red}{-60x} +24 \\\Leftrightarrow & 500x \color{red}{+125} \color{blue}{-125} \color{blue}{+60x} & = & \color{red}{-60x} +24 \color{blue}{+60x} \color{blue}{-125} \\\Leftrightarrow & 500x+60x& = & 24-125 \\\Leftrightarrow & \color{red}{560} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{560} & & \\ & V = \left\{ \frac{-101}{560} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{10}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-50} & = & \color{red}{385x} +44 \\\Leftrightarrow & 825x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & 825x-385x& = & 44+50 \\\Leftrightarrow & \color{red}{440} x& = & 94 \\\Leftrightarrow & x = \frac{94}{440} & & \\\Leftrightarrow & x = \frac{47}{220} & & \\ & V = \left\{ \frac{47}{220} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+180} & = & \color{red}{-567x} +56 \\\Leftrightarrow & -1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{-180} \\\Leftrightarrow & -1260x+567x& = & 56-180 \\\Leftrightarrow & \color{red}{-693} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{-693} & & \\\Leftrightarrow & x = \frac{124}{693} & & \\ & V = \left\{ \frac{124}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{3})& = & 4x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{14}{3}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+28} & = & \color{red}{24x} +15 \\\Leftrightarrow & -168x \color{red}{+28} \color{blue}{-28} \color{blue}{-24x} & = & \color{red}{24x} +15 \color{blue}{-24x} \color{blue}{-28} \\\Leftrightarrow & -168x-24x& = & 15-28 \\\Leftrightarrow & \color{red}{-192} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-192} & & \\\Leftrightarrow & x = \frac{13}{192} & & \\ & V = \left\{ \frac{13}{192} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{2})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{15}{2}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{30}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{4}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 30x \color{red}{-15} & = & \color{red}{4x} +3 \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = & \color{red}{4x} +3 \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 30x-4x& = & 3+15 \\\Leftrightarrow & \color{red}{26} x& = & 18 \\\Leftrightarrow & x = \frac{18}{26} & & \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{245x} +15 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +15 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & 1050x-245x& = & 15-84 \\\Leftrightarrow & \color{red}{805} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{805} & & \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1980}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1980x \color{red}{+180} & = & \color{red}{990x} +99 \\\Leftrightarrow & -1980x \color{red}{+180} \color{blue}{-180} \color{blue}{-990x} & = & \color{red}{990x} +99 \color{blue}{-990x} \color{blue}{-180} \\\Leftrightarrow & -1980x-990x& = & 99-180 \\\Leftrightarrow & \color{red}{-2970} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-2970} & & \\\Leftrightarrow & x = \frac{3}{110} & & \\ & V = \left\{ \frac{3}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -16x+\frac{12}{11}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+12} & = & \color{red}{-77x} +7 \\\Leftrightarrow & -176x \color{red}{+12} \color{blue}{-12} \color{blue}{+77x} & = & \color{red}{-77x} +7 \color{blue}{+77x} \color{blue}{-12} \\\Leftrightarrow & -176x+77x& = & 7-12 \\\Leftrightarrow & \color{red}{-99} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-99} & & \\\Leftrightarrow & x = \frac{5}{99} & & \\ & V = \left\{ \frac{5}{99} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-231} & = & \color{red}{-264x} +48 \\\Leftrightarrow & 2464x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +48 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & 2464x+264x& = & 48+231 \\\Leftrightarrow & \color{red}{2728} x& = & 279 \\\Leftrightarrow & x = \frac{279}{2728} & & \\\Leftrightarrow & x = \frac{9}{88} & & \\ & V = \left\{ \frac{9}{88} \right\} & \\\end{align}\)
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