Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{21x} +4 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & 36x-21x& = & 4-8 \\\Leftrightarrow & \color{red}{15} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-840}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -840x \color{red}{+72} & = & \color{red}{-588x} +49 \\\Leftrightarrow & -840x \color{red}{+72} \color{blue}{-72} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{-72} \\\Leftrightarrow & -840x+588x& = & 49-72 \\\Leftrightarrow & \color{red}{-252} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-252} & & \\\Leftrightarrow & x = \frac{23}{252} & & \\ & V = \left\{ \frac{23}{252} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{+16} & = & \color{red}{90x} +27 \\\Leftrightarrow & 108x \color{red}{+16} \color{blue}{-16} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-16} \\\Leftrightarrow & 108x-90x& = & 27-16 \\\Leftrightarrow & \color{red}{18} x& = & 11 \\\Leftrightarrow & x = \frac{11}{18} & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{8})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{35}{8}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-175} & = & \color{red}{-360x} +64 \\\Leftrightarrow & 560x \color{red}{-175} \color{blue}{+175} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{+175} \\\Leftrightarrow & 560x+360x& = & 64+175 \\\Leftrightarrow & \color{red}{920} x& = & 239 \\\Leftrightarrow & x = \frac{239}{920} & & \\ & V = \left\{ \frac{239}{920} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -495x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -495x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{-110} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-110} & & \\\Leftrightarrow & x = \frac{-81}{55} & & \\ & V = \left\{ \frac{-81}{55} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & -9x+\frac{9}{8} \\\Leftrightarrow & 20x-\frac{10}{7}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-80} & = & \color{red}{-504x} +63 \\\Leftrightarrow & 1120x \color{red}{-80} \color{blue}{+80} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{+80} \\\Leftrightarrow & 1120x+504x& = & 63+80 \\\Leftrightarrow & \color{red}{1624} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1624} & & \\ & V = \left\{ \frac{143}{1624} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -9x+\frac{12}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{+48} & = & \color{red}{196x} +21 \\\Leftrightarrow & -252x \color{red}{+48} \color{blue}{-48} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-48} \\\Leftrightarrow & -252x-196x& = & 21-48 \\\Leftrightarrow & \color{red}{-448} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-448} & & \\\Leftrightarrow & x = \frac{27}{448} & & \\ & V = \left\{ \frac{27}{448} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{231x} +30 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 660x-231x& = & 30-220 \\\Leftrightarrow & \color{red}{429} x& = & -190 \\\Leftrightarrow & x = \frac{-190}{429} & & \\ & V = \left\{ \frac{-190}{429} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{11})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{35}{11}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-105} & = & \color{red}{-297x} +110 \\\Leftrightarrow & 462x \color{red}{-105} \color{blue}{+105} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+105} \\\Leftrightarrow & 462x+297x& = & 110+105 \\\Leftrightarrow & \color{red}{759} x& = & 215 \\\Leftrightarrow & x = \frac{215}{759} & & \\ & V = \left\{ \frac{215}{759} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & 4x+\frac{3}{8} \\\Leftrightarrow & 21x-\frac{21}{11}& = & 4x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x- \frac{168}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{-168} & = & \color{red}{352x} +33 \\\Leftrightarrow & 1848x \color{red}{-168} \color{blue}{+168} \color{blue}{-352x} & = & \color{red}{352x} +33 \color{blue}{-352x} \color{blue}{+168} \\\Leftrightarrow & 1848x-352x& = & 33+168 \\\Leftrightarrow & \color{red}{1496} x& = & 201 \\\Leftrightarrow & x = \frac{201}{1496} & & \\ & V = \left\{ \frac{201}{1496} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{8}{9}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-16} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -216x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & -216x+90x& = & 45+16 \\\Leftrightarrow & \color{red}{-126} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-126} & & \\\Leftrightarrow & x = \frac{-61}{126} & & \\ & V = \left\{ \frac{-61}{126} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{3})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-42} & = & \color{red}{-27x} +10 \\\Leftrightarrow & 126x \color{red}{-42} \color{blue}{+42} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{+42} \\\Leftrightarrow & 126x+27x& = & 10+42 \\\Leftrightarrow & \color{red}{153} x& = & 52 \\\Leftrightarrow & x = \frac{52}{153} & & \\ & V = \left\{ \frac{52}{153} \right\} & \\\end{align}\)
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