Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-20} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 70x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & 70x+49x& = & 10+20 \\\Leftrightarrow & \color{red}{119} x& = & 30 \\\Leftrightarrow & x = \frac{30}{119} & & \\ & V = \left\{ \frac{30}{119} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{4})& = & 4x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+135} & = & \color{red}{144x} +32 \\\Leftrightarrow & 540x \color{red}{+135} \color{blue}{-135} \color{blue}{-144x} & = & \color{red}{144x} +32 \color{blue}{-144x} \color{blue}{-135} \\\Leftrightarrow & 540x-144x& = & 32-135 \\\Leftrightarrow & \color{red}{396} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{396} & & \\ & V = \left\{ \frac{-103}{396} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{315x} +20 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-36} \\\Leftrightarrow & -270x-315x& = & 20-36 \\\Leftrightarrow & \color{red}{-585} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-585} & & \\\Leftrightarrow & x = \frac{16}{585} & & \\ & V = \left\{ \frac{16}{585} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{18}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-18} & = & \color{red}{-140x} +45 \\\Leftrightarrow & -180x \color{red}{-18} \color{blue}{+18} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{+18} \\\Leftrightarrow & -180x+140x& = & 45+18 \\\Leftrightarrow & \color{red}{-40} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-40} & & \\\Leftrightarrow & x = \frac{-63}{40} & & \\ & V = \left\{ \frac{-63}{40} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-70} & = & \color{red}{693x} +33 \\\Leftrightarrow & 308x \color{red}{-70} \color{blue}{+70} \color{blue}{-693x} & = & \color{red}{693x} +33 \color{blue}{-693x} \color{blue}{+70} \\\Leftrightarrow & 308x-693x& = & 33+70 \\\Leftrightarrow & \color{red}{-385} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-385} & & \\\Leftrightarrow & x = \frac{-103}{385} & & \\ & V = \left\{ \frac{-103}{385} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{4}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+44} & = & \color{red}{275x} +30 \\\Leftrightarrow & 330x \color{red}{+44} \color{blue}{-44} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-44} \\\Leftrightarrow & 330x-275x& = & 30-44 \\\Leftrightarrow & \color{red}{55} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{55} & & \\ & V = \left\{ \frac{-14}{55} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{9})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+56} & = & \color{red}{441x} +72 \\\Leftrightarrow & -630x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +72 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -630x-441x& = & 72-56 \\\Leftrightarrow & \color{red}{-1071} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-1071} & & \\\Leftrightarrow & x = \frac{-16}{1071} & & \\ & V = \left\{ \frac{-16}{1071} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{8}{3}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-40} & = & \color{red}{-45x} +12 \\\Leftrightarrow & 300x \color{red}{-40} \color{blue}{+40} \color{blue}{+45x} & = & \color{red}{-45x} +12 \color{blue}{+45x} \color{blue}{+40} \\\Leftrightarrow & 300x+45x& = & 12+40 \\\Leftrightarrow & \color{red}{345} x& = & 52 \\\Leftrightarrow & x = \frac{52}{345} & & \\ & V = \left\{ \frac{52}{345} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -300x+105x& = & 40-36 \\\Leftrightarrow & \color{red}{-195} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-195} & & \\\Leftrightarrow & x = \frac{-4}{195} & & \\ & V = \left\{ \frac{-4}{195} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{9})& = & 3x+\frac{7}{11} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-44} & = & \color{red}{297x} +63 \\\Leftrightarrow & 792x \color{red}{-44} \color{blue}{+44} \color{blue}{-297x} & = & \color{red}{297x} +63 \color{blue}{-297x} \color{blue}{+44} \\\Leftrightarrow & 792x-297x& = & 63+44 \\\Leftrightarrow & \color{red}{495} x& = & 107 \\\Leftrightarrow & x = \frac{107}{495} & & \\ & V = \left\{ \frac{107}{495} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{11})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-15} & = & \color{red}{88x} +5 \\\Leftrightarrow & -165x \color{red}{-15} \color{blue}{+15} \color{blue}{-88x} & = & \color{red}{88x} +5 \color{blue}{-88x} \color{blue}{+15} \\\Leftrightarrow & -165x-88x& = & 5+15 \\\Leftrightarrow & \color{red}{-253} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-253} & & \\\Leftrightarrow & x = \frac{-20}{253} & & \\ & V = \left\{ \frac{-20}{253} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 24x-\frac{12}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-84} & = & \color{red}{385x} +22 \\\Leftrightarrow & 1848x \color{red}{-84} \color{blue}{+84} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+84} \\\Leftrightarrow & 1848x-385x& = & 22+84 \\\Leftrightarrow & \color{red}{1463} x& = & 106 \\\Leftrightarrow & x = \frac{106}{1463} & & \\ & V = \left\{ \frac{106}{1463} \right\} & \\\end{align}\)
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