Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +2 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 2+10 \\\Leftrightarrow & \color{red}{-119} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-119} & & \\\Leftrightarrow & x = \frac{-12}{119} & & \\ & V = \left\{ \frac{-12}{119} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-264}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} })& = & (\frac{-594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{-594x} +55 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{+594x} & = & \color{red}{-594x} +55 \color{blue}{+594x} \color{blue}{-60} \\\Leftrightarrow & -264x+594x& = & 55-60 \\\Leftrightarrow & \color{red}{330} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{330} & & \\\Leftrightarrow & x = \frac{-1}{66} & & \\ & V = \left\{ \frac{-1}{66} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+54} & = & \color{red}{567x} +14 \\\Leftrightarrow & -504x \color{red}{+54} \color{blue}{-54} \color{blue}{-567x} & = & \color{red}{567x} +14 \color{blue}{-567x} \color{blue}{-54} \\\Leftrightarrow & -504x-567x& = & 14-54 \\\Leftrightarrow & \color{red}{-1071} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1071} & & \\\Leftrightarrow & x = \frac{40}{1071} & & \\ & V = \left\{ \frac{40}{1071} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-180} & = & \color{red}{-441x} +35 \\\Leftrightarrow & 1260x \color{red}{-180} \color{blue}{+180} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{+180} \\\Leftrightarrow & 1260x+441x& = & 35+180 \\\Leftrightarrow & \color{red}{1701} x& = & 215 \\\Leftrightarrow & x = \frac{215}{1701} & & \\ & V = \left\{ \frac{215}{1701} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -180x+75x& = & 20+36 \\\Leftrightarrow & \color{red}{-105} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-105} & & \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-420}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -420x \color{red}{+60} & = & \color{red}{294x} +49 \\\Leftrightarrow & -420x \color{red}{+60} \color{blue}{-60} \color{blue}{-294x} & = & \color{red}{294x} +49 \color{blue}{-294x} \color{blue}{-60} \\\Leftrightarrow & -420x-294x& = & 49-60 \\\Leftrightarrow & \color{red}{-714} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-714} & & \\\Leftrightarrow & x = \frac{11}{714} & & \\ & V = \left\{ \frac{11}{714} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{5})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x-\frac{14}{5}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{-14} & = & \color{red}{-15x} +8 \\\Leftrightarrow & -70x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & -70x+15x& = & 8+14 \\\Leftrightarrow & \color{red}{-55} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-55} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{5})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 35x+\frac{14}{5}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{175}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 175x \color{red}{+14} & = & \color{red}{-10x} +2 \\\Leftrightarrow & 175x \color{red}{+14} \color{blue}{-14} \color{blue}{+10x} & = & \color{red}{-10x} +2 \color{blue}{+10x} \color{blue}{-14} \\\Leftrightarrow & 175x+10x& = & 2-14 \\\Leftrightarrow & \color{red}{185} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{185} & & \\ & V = \left\{ \frac{-12}{185} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{15}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-504}{ \color{blue}{42} }x+ \frac{90}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -504x \color{red}{+90} & = & \color{red}{210x} +35 \\\Leftrightarrow & -504x \color{red}{+90} \color{blue}{-90} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{-90} \\\Leftrightarrow & -504x-210x& = & 35-90 \\\Leftrightarrow & \color{red}{-714} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-714} & & \\\Leftrightarrow & x = \frac{55}{714} & & \\ & V = \left\{ \frac{55}{714} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -9x-\frac{6}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x- \frac{48}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{-48} & = & \color{red}{616x} +77 \\\Leftrightarrow & -792x \color{red}{-48} \color{blue}{+48} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+48} \\\Leftrightarrow & -792x-616x& = & 77+48 \\\Leftrightarrow & \color{red}{-1408} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-1408} & & \\\Leftrightarrow & x = \frac{-125}{1408} & & \\ & V = \left\{ \frac{-125}{1408} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -4x-\frac{4}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+12} \\\Leftrightarrow & -60x+135x& = & 10+12 \\\Leftrightarrow & \color{red}{75} x& = & 22 \\\Leftrightarrow & x = \frac{22}{75} & & \\ & V = \left\{ \frac{22}{75} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{-48} & = & \color{red}{-140x} +15 \\\Leftrightarrow & -600x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -600x+140x& = & 15+48 \\\Leftrightarrow & \color{red}{-460} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-460} & & \\\Leftrightarrow & x = \frac{-63}{460} & & \\ & V = \left\{ \frac{-63}{460} \right\} & \\\end{align}\)
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