Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{8})& = & -8x+\frac{4}{3} \\\Leftrightarrow & 21x+\frac{35}{8}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{105}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+105} & = & \color{red}{-192x} +32 \\\Leftrightarrow & 504x \color{red}{+105} \color{blue}{-105} \color{blue}{+192x} & = & \color{red}{-192x} +32 \color{blue}{+192x} \color{blue}{-105} \\\Leftrightarrow & 504x+192x& = & 32-105 \\\Leftrightarrow & \color{red}{696} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{696} & & \\ & V = \left\{ \frac{-73}{696} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & -9x+\frac{7}{9} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{-81x} +7 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{+81x} & = & \color{red}{-81x} +7 \color{blue}{+81x} \color{blue}{+28} \\\Leftrightarrow & 252x+81x& = & 7+28 \\\Leftrightarrow & \color{red}{333} x& = & 35 \\\Leftrightarrow & x = \frac{35}{333} & & \\ & V = \left\{ \frac{35}{333} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{+15} & = & \color{red}{40x} +3 \\\Leftrightarrow & 96x \color{red}{+15} \color{blue}{-15} \color{blue}{-40x} & = & \color{red}{40x} +3 \color{blue}{-40x} \color{blue}{-15} \\\Leftrightarrow & 96x-40x& = & 3-15 \\\Leftrightarrow & \color{red}{56} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{56} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 4x-\frac{8}{9}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{-693x} +90 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +90 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & 396x+693x& = & 90+88 \\\Leftrightarrow & \color{red}{1089} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1089} & & \\ & V = \left\{ \frac{178}{1089} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+54} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 990x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & 990x+231x& = & 88-54 \\\Leftrightarrow & \color{red}{1221} x& = & 34 \\\Leftrightarrow & x = \frac{34}{1221} & & \\ & V = \left\{ \frac{34}{1221} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+88} & = & \color{red}{-891x} +54 \\\Leftrightarrow & 1980x \color{red}{+88} \color{blue}{-88} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{-88} \\\Leftrightarrow & 1980x+891x& = & 54-88 \\\Leftrightarrow & \color{red}{2871} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{2871} & & \\ & V = \left\{ \frac{-34}{2871} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{35x} +7 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +7 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 75x-35x& = & 7-12 \\\Leftrightarrow & \color{red}{40} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{40} & & \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-72} & = & \color{red}{105x} +40 \\\Leftrightarrow & 450x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & 450x-105x& = & 40+72 \\\Leftrightarrow & \color{red}{345} x& = & 112 \\\Leftrightarrow & x = \frac{112}{345} & & \\ & V = \left\{ \frac{112}{345} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{7}{4} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-96x} +21 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+96x} & = & \color{red}{-96x} +21 \color{blue}{+96x} \color{blue}{+56} \\\Leftrightarrow & -252x+96x& = & 21+56 \\\Leftrightarrow & \color{red}{-156} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-156} & & \\\Leftrightarrow & x = \frac{-77}{156} & & \\ & V = \left\{ \frac{-77}{156} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x+ \frac{96}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{+96} & = & \color{red}{140x} +63 \\\Leftrightarrow & 672x \color{red}{+96} \color{blue}{-96} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-96} \\\Leftrightarrow & 672x-140x& = & 63-96 \\\Leftrightarrow & \color{red}{532} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{532} & & \\ & V = \left\{ \frac{-33}{532} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{210x} +25 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-210x} & = & \color{red}{210x} +25 \color{blue}{-210x} \color{blue}{-72} \\\Leftrightarrow & 450x-210x& = & 25-72 \\\Leftrightarrow & \color{red}{240} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{240} & & \\ & V = \left\{ \frac{-47}{240} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{12})& = & 4x+\frac{7}{5} \\\Leftrightarrow & -15x-\frac{25}{12}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-900}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{240}{ \color{blue}{60} }x+ \frac{84}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -900x \color{red}{-125} & = & \color{red}{240x} +84 \\\Leftrightarrow & -900x \color{red}{-125} \color{blue}{+125} \color{blue}{-240x} & = & \color{red}{240x} +84 \color{blue}{-240x} \color{blue}{+125} \\\Leftrightarrow & -900x-240x& = & 84+125 \\\Leftrightarrow & \color{red}{-1140} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-1140} & & \\\Leftrightarrow & x = \frac{-11}{60} & & \\ & V = \left\{ \frac{-11}{60} \right\} & \\\end{align}\)
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