Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{11})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{15}{11}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x+ \frac{135}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{+135} & = & \color{red}{792x} +44 \\\Leftrightarrow & -1485x \color{red}{+135} \color{blue}{-135} \color{blue}{-792x} & = & \color{red}{792x} +44 \color{blue}{-792x} \color{blue}{-135} \\\Leftrightarrow & -1485x-792x& = & 44-135 \\\Leftrightarrow & \color{red}{-2277} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{-2277} & & \\\Leftrightarrow & x = \frac{91}{2277} & & \\ & V = \left\{ \frac{91}{2277} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{4}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{12}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-12} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -126x \color{red}{-12} \color{blue}{+12} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+12} \\\Leftrightarrow & -126x+147x& = & 14+12 \\\Leftrightarrow & \color{red}{21} x& = & 26 \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{+60} & = & \color{red}{210x} +63 \\\Leftrightarrow & 280x \color{red}{+60} \color{blue}{-60} \color{blue}{-210x} & = & \color{red}{210x} +63 \color{blue}{-210x} \color{blue}{-60} \\\Leftrightarrow & 280x-210x& = & 63-60 \\\Leftrightarrow & \color{red}{70} x& = & 3 \\\Leftrightarrow & x = \frac{3}{70} & & \\ & V = \left\{ \frac{3}{70} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{11})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 4x+\frac{6}{11}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{-297x} +88 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-54} \\\Leftrightarrow & 396x+297x& = & 88-54 \\\Leftrightarrow & \color{red}{693} x& = & 34 \\\Leftrightarrow & x = \frac{34}{693} & & \\ & V = \left\{ \frac{34}{693} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -16x-\frac{16}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x- \frac{112}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{-112} & = & \color{red}{-245x} +15 \\\Leftrightarrow & -560x \color{red}{-112} \color{blue}{+112} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{+112} \\\Leftrightarrow & -560x+245x& = & 15+112 \\\Leftrightarrow & \color{red}{-315} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-315} & & \\\Leftrightarrow & x = \frac{-127}{315} & & \\ & V = \left\{ \frac{-127}{315} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{245x} +28 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+150} \\\Leftrightarrow & 630x-245x& = & 28+150 \\\Leftrightarrow & \color{red}{385} x& = & 178 \\\Leftrightarrow & x = \frac{178}{385} & & \\ & V = \left\{ \frac{178}{385} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{280x} +30 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{-280x} & = & \color{red}{280x} +30 \color{blue}{-280x} \color{blue}{+84} \\\Leftrightarrow & 525x-280x& = & 30+84 \\\Leftrightarrow & \color{red}{245} x& = & 114 \\\Leftrightarrow & x = \frac{114}{245} & & \\ & V = \left\{ \frac{114}{245} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & -2x+\frac{10}{9} \\\Leftrightarrow & -28x-\frac{35}{9}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-35} & = & \color{red}{-18x} +10 \\\Leftrightarrow & -252x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +10 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & -252x+18x& = & 10+35 \\\Leftrightarrow & \color{red}{-234} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-234} & & \\\Leftrightarrow & x = \frac{-5}{26} & & \\ & V = \left\{ \frac{-5}{26} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{-264x} +64 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +64 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & -1232x+264x& = & 64+231 \\\Leftrightarrow & \color{red}{-968} x& = & 295 \\\Leftrightarrow & x = \frac{295}{-968} & & \\\Leftrightarrow & x = \frac{-295}{968} & & \\ & V = \left\{ \frac{-295}{968} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{8}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+72} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1188x \color{red}{+72} \color{blue}{-72} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-72} \\\Leftrightarrow & 1188x+693x& = & 110-72 \\\Leftrightarrow & \color{red}{1881} x& = & 38 \\\Leftrightarrow & x = \frac{38}{1881} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{35x} +3 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -100x-35x& = & 3+12 \\\Leftrightarrow & \color{red}{-135} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-135} & & \\\Leftrightarrow & x = \frac{-1}{9} & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+132} & = & \color{red}{385x} +15 \\\Leftrightarrow & 440x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 440x-385x& = & 15-132 \\\Leftrightarrow & \color{red}{55} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{55} & & \\ & V = \left\{ \frac{-117}{55} \right\} & \\\end{align}\)
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