Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{5})& = & -6x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{21}{5}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x+ \frac{231}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{+231} & = & \color{red}{-330x} +30 \\\Leftrightarrow & 1925x \color{red}{+231} \color{blue}{-231} \color{blue}{+330x} & = & \color{red}{-330x} +30 \color{blue}{+330x} \color{blue}{-231} \\\Leftrightarrow & 1925x+330x& = & 30-231 \\\Leftrightarrow & \color{red}{2255} x& = & -201 \\\Leftrightarrow & x = \frac{-201}{2255} & & \\ & V = \left\{ \frac{-201}{2255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{16}{3}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{112}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+112} & = & \color{red}{-189x} +6 \\\Leftrightarrow & -168x \color{red}{+112} \color{blue}{-112} \color{blue}{+189x} & = & \color{red}{-189x} +6 \color{blue}{+189x} \color{blue}{-112} \\\Leftrightarrow & -168x+189x& = & 6-112 \\\Leftrightarrow & \color{red}{21} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{21} & & \\ & V = \left\{ \frac{-106}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +10 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 10+132 \\\Leftrightarrow & \color{red}{385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{385} & & \\ & V = \left\{ \frac{142}{385} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -12x+\frac{6}{11}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+6} & = & \color{red}{-55x} +8 \\\Leftrightarrow & -132x \color{red}{+6} \color{blue}{-6} \color{blue}{+55x} & = & \color{red}{-55x} +8 \color{blue}{+55x} \color{blue}{-6} \\\Leftrightarrow & -132x+55x& = & 8-6 \\\Leftrightarrow & \color{red}{-77} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-77} & & \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -8x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+66} & = & \color{red}{-616x} +56 \\\Leftrightarrow & 693x \color{red}{+66} \color{blue}{-66} \color{blue}{+616x} & = & \color{red}{-616x} +56 \color{blue}{+616x} \color{blue}{-66} \\\Leftrightarrow & 693x+616x& = & 56-66 \\\Leftrightarrow & \color{red}{1309} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{1309} & & \\ & V = \left\{ \frac{-10}{1309} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{8})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x+\frac{35}{8}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{175}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+175} & = & \color{red}{-120x} +64 \\\Leftrightarrow & -560x \color{red}{+175} \color{blue}{-175} \color{blue}{+120x} & = & \color{red}{-120x} +64 \color{blue}{+120x} \color{blue}{-175} \\\Leftrightarrow & -560x+120x& = & 64-175 \\\Leftrightarrow & \color{red}{-440} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{-440} & & \\\Leftrightarrow & x = \frac{111}{440} & & \\ & V = \left\{ \frac{111}{440} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -6x+\frac{6}{7} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{-126x} +18 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{+126x} & = & \color{red}{-126x} +18 \color{blue}{+126x} \color{blue}{-98} \\\Leftrightarrow & 735x+126x& = & 18-98 \\\Leftrightarrow & \color{red}{861} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{861} & & \\ & V = \left\{ \frac{-80}{861} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{11})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -25x-\frac{10}{11}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-30} & = & \color{red}{-231x} +55 \\\Leftrightarrow & -825x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -825x+231x& = & 55+30 \\\Leftrightarrow & \color{red}{-594} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-594} & & \\\Leftrightarrow & x = \frac{-85}{594} & & \\ & V = \left\{ \frac{-85}{594} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+132} & = & \color{red}{-165x} +25 \\\Leftrightarrow & -1100x \color{red}{+132} \color{blue}{-132} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{-132} \\\Leftrightarrow & -1100x+165x& = & 25-132 \\\Leftrightarrow & \color{red}{-935} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-935} & & \\\Leftrightarrow & x = \frac{107}{935} & & \\ & V = \left\{ \frac{107}{935} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{-48} & = & \color{red}{70x} +7 \\\Leftrightarrow & -300x \color{red}{-48} \color{blue}{+48} \color{blue}{-70x} & = & \color{red}{70x} +7 \color{blue}{-70x} \color{blue}{+48} \\\Leftrightarrow & -300x-70x& = & 7+48 \\\Leftrightarrow & \color{red}{-370} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-370} & & \\\Leftrightarrow & x = \frac{-11}{74} & & \\ & V = \left\{ \frac{-11}{74} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{8})& = & -8x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{25}{8}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{125}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+125} & = & \color{red}{-320x} +36 \\\Leftrightarrow & 600x \color{red}{+125} \color{blue}{-125} \color{blue}{+320x} & = & \color{red}{-320x} +36 \color{blue}{+320x} \color{blue}{-125} \\\Leftrightarrow & 600x+320x& = & 36-125 \\\Leftrightarrow & \color{red}{920} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{920} & & \\ & V = \left\{ \frac{-89}{920} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{7})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -4x-\frac{8}{7}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-280}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{-80} & = & \color{red}{350x} +49 \\\Leftrightarrow & -280x \color{red}{-80} \color{blue}{+80} \color{blue}{-350x} & = & \color{red}{350x} +49 \color{blue}{-350x} \color{blue}{+80} \\\Leftrightarrow & -280x-350x& = & 49+80 \\\Leftrightarrow & \color{red}{-630} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-630} & & \\\Leftrightarrow & x = \frac{-43}{210} & & \\ & V = \left\{ \frac{-43}{210} \right\} & \\\end{align}\)
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