Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & -630x+147x& = & 70-90 \\\Leftrightarrow & \color{red}{-483} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-483} & & \\\Leftrightarrow & x = \frac{20}{483} & & \\ & V = \left\{ \frac{20}{483} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{3})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -8x+\frac{4}{3}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+8} & = & \color{red}{-18x} +5 \\\Leftrightarrow & -48x \color{red}{+8} \color{blue}{-8} \color{blue}{+18x} & = & \color{red}{-18x} +5 \color{blue}{+18x} \color{blue}{-8} \\\Leftrightarrow & -48x+18x& = & 5-8 \\\Leftrightarrow & \color{red}{-30} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-30} & & \\\Leftrightarrow & x = \frac{1}{10} & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{-405x} +36 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{+405x} & = & \color{red}{-405x} +36 \color{blue}{+405x} \color{blue}{+40} \\\Leftrightarrow & 360x+405x& = & 36+40 \\\Leftrightarrow & \color{red}{765} x& = & 76 \\\Leftrightarrow & x = \frac{76}{765} & & \\ & V = \left\{ \frac{76}{765} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 4x+\frac{8}{9} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-54} & = & \color{red}{252x} +56 \\\Leftrightarrow & 945x \color{red}{-54} \color{blue}{+54} \color{blue}{-252x} & = & \color{red}{252x} +56 \color{blue}{-252x} \color{blue}{+54} \\\Leftrightarrow & 945x-252x& = & 56+54 \\\Leftrightarrow & \color{red}{693} x& = & 110 \\\Leftrightarrow & x = \frac{110}{693} & & \\\Leftrightarrow & x = \frac{10}{63} & & \\ & V = \left\{ \frac{10}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{4}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+28} & = & \color{red}{175x} +20 \\\Leftrightarrow & 210x \color{red}{+28} \color{blue}{-28} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-28} \\\Leftrightarrow & 210x-175x& = & 20-28 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{245x} +20 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -210x-245x& = & 20-84 \\\Leftrightarrow & \color{red}{-455} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-455} & & \\\Leftrightarrow & x = \frac{64}{455} & & \\ & V = \left\{ \frac{64}{455} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-44} & = & \color{red}{693x} +54 \\\Leftrightarrow & -594x \color{red}{-44} \color{blue}{+44} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+44} \\\Leftrightarrow & -594x-693x& = & 54+44 \\\Leftrightarrow & \color{red}{-1287} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-1287} & & \\\Leftrightarrow & x = \frac{-98}{1287} & & \\ & V = \left\{ \frac{-98}{1287} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{8}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{64}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-64} & = & \color{red}{440x} +99 \\\Leftrightarrow & -1056x \color{red}{-64} \color{blue}{+64} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{+64} \\\Leftrightarrow & -1056x-440x& = & 99+64 \\\Leftrightarrow & \color{red}{-1496} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-1496} & & \\\Leftrightarrow & x = \frac{-163}{1496} & & \\ & V = \left\{ \frac{-163}{1496} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{55x} +2 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & -132x-55x& = & 2+18 \\\Leftrightarrow & \color{red}{-187} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-187} & & \\\Leftrightarrow & x = \frac{-20}{187} & & \\ & V = \left\{ \frac{-20}{187} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{3})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{-63x} +4 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & 180x+63x& = & 4-24 \\\Leftrightarrow & \color{red}{243} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{243} & & \\ & V = \left\{ \frac{-20}{243} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & -4x+\frac{4}{5} \\\Leftrightarrow & -15x+\frac{15}{8}& = & -4x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-160}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{+75} & = & \color{red}{-160x} +32 \\\Leftrightarrow & -600x \color{red}{+75} \color{blue}{-75} \color{blue}{+160x} & = & \color{red}{-160x} +32 \color{blue}{+160x} \color{blue}{-75} \\\Leftrightarrow & -600x+160x& = & 32-75 \\\Leftrightarrow & \color{red}{-440} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-440} & & \\\Leftrightarrow & x = \frac{43}{440} & & \\ & V = \left\{ \frac{43}{440} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & -84x+35x& = & 9-30 \\\Leftrightarrow & \color{red}{-49} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-49} & & \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
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