Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+80} & = & \color{red}{-270x} +21 \\\Leftrightarrow & 600x \color{red}{+80} \color{blue}{-80} \color{blue}{+270x} & = & \color{red}{-270x} +21 \color{blue}{+270x} \color{blue}{-80} \\\Leftrightarrow & 600x+270x& = & 21-80 \\\Leftrightarrow & \color{red}{870} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{870} & & \\ & V = \left\{ \frac{-59}{870} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{20}{3}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-140} & = & \color{red}{105x} +9 \\\Leftrightarrow & 252x \color{red}{-140} \color{blue}{+140} \color{blue}{-105x} & = & \color{red}{105x} +9 \color{blue}{-105x} \color{blue}{+140} \\\Leftrightarrow & 252x-105x& = & 9+140 \\\Leftrightarrow & \color{red}{147} x& = & 149 \\\Leftrightarrow & x = \frac{149}{147} & & \\ & V = \left\{ \frac{149}{147} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{-100} & = & \color{red}{120x} +18 \\\Leftrightarrow & 375x \color{red}{-100} \color{blue}{+100} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{+100} \\\Leftrightarrow & 375x-120x& = & 18+100 \\\Leftrightarrow & \color{red}{255} x& = & 118 \\\Leftrightarrow & x = \frac{118}{255} & & \\ & V = \left\{ \frac{118}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-24} & = & \color{red}{231x} +22 \\\Leftrightarrow & -660x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -660x-231x& = & 22+24 \\\Leftrightarrow & \color{red}{-891} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-891} & & \\\Leftrightarrow & x = \frac{-46}{891} & & \\ & V = \left\{ \frac{-46}{891} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-100} & = & \color{red}{120x} +18 \\\Leftrightarrow & 225x \color{red}{-100} \color{blue}{+100} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{+100} \\\Leftrightarrow & 225x-120x& = & 18+100 \\\Leftrightarrow & \color{red}{105} x& = & 118 \\\Leftrightarrow & x = \frac{118}{105} & & \\ & V = \left\{ \frac{118}{105} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{-165x} +30 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{+165x} & = & \color{red}{-165x} +30 \color{blue}{+165x} \color{blue}{+132} \\\Leftrightarrow & 880x+165x& = & 30+132 \\\Leftrightarrow & \color{red}{1045} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1045} & & \\ & V = \left\{ \frac{162}{1045} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+72} & = & \color{red}{105x} +10 \\\Leftrightarrow & 360x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 360x-105x& = & 10-72 \\\Leftrightarrow & \color{red}{255} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{255} & & \\ & V = \left\{ \frac{-62}{255} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +4 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 4+12 \\\Leftrightarrow & \color{red}{-85} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-85} & & \\\Leftrightarrow & x = \frac{-16}{85} & & \\ & V = \left\{ \frac{-16}{85} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-18} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -330x \color{red}{-18} \color{blue}{+18} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+18} \\\Leftrightarrow & -330x+231x& = & 88+18 \\\Leftrightarrow & \color{red}{-99} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-99} & & \\\Leftrightarrow & x = \frac{-106}{99} & & \\ & V = \left\{ \frac{-106}{99} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-80} & = & \color{red}{175x} +49 \\\Leftrightarrow & 420x \color{red}{-80} \color{blue}{+80} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{+80} \\\Leftrightarrow & 420x-175x& = & 49+80 \\\Leftrightarrow & \color{red}{245} x& = & 129 \\\Leftrightarrow & x = \frac{129}{245} & & \\ & V = \left\{ \frac{129}{245} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{2})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -25x+\frac{15}{2}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{+45} & = & \color{red}{54x} +4 \\\Leftrightarrow & -150x \color{red}{+45} \color{blue}{-45} \color{blue}{-54x} & = & \color{red}{54x} +4 \color{blue}{-54x} \color{blue}{-45} \\\Leftrightarrow & -150x-54x& = & 4-45 \\\Leftrightarrow & \color{red}{-204} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-204} & & \\\Leftrightarrow & x = \frac{41}{204} & & \\ & V = \left\{ \frac{41}{204} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+168} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -1050x \color{red}{+168} \color{blue}{-168} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-168} \\\Leftrightarrow & -1050x+245x& = & 50-168 \\\Leftrightarrow & \color{red}{-805} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-805} & & \\\Leftrightarrow & x = \frac{118}{805} & & \\ & V = \left\{ \frac{118}{805} \right\} & \\\end{align}\)
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