Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -20x-\frac{8}{9}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-56} & = & \color{red}{-441x} +54 \\\Leftrightarrow & -1260x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +54 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & -1260x+441x& = & 54+56 \\\Leftrightarrow & \color{red}{-819} x& = & 110 \\\Leftrightarrow & x = \frac{110}{-819} & & \\\Leftrightarrow & x = \frac{-110}{819} & & \\ & V = \left\{ \frac{-110}{819} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{10})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 9x-\frac{9}{10}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 10 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x- \frac{36}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{-36} & = & \color{red}{-200x} +25 \\\Leftrightarrow & 360x \color{red}{-36} \color{blue}{+36} \color{blue}{+200x} & = & \color{red}{-200x} +25 \color{blue}{+200x} \color{blue}{+36} \\\Leftrightarrow & 360x+200x& = & 25+36 \\\Leftrightarrow & \color{red}{560} x& = & 61 \\\Leftrightarrow & x = \frac{61}{560} & & \\ & V = \left\{ \frac{61}{560} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{12}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-60} & = & \color{red}{275x} +66 \\\Leftrightarrow & 990x \color{red}{-60} \color{blue}{+60} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+60} \\\Leftrightarrow & 990x-275x& = & 66+60 \\\Leftrightarrow & \color{red}{715} x& = & 126 \\\Leftrightarrow & x = \frac{126}{715} & & \\ & V = \left\{ \frac{126}{715} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 20x-\frac{8}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{-64} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 480x \color{red}{-64} \color{blue}{+64} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+64} \\\Leftrightarrow & 480x+72x& = & 21+64 \\\Leftrightarrow & \color{red}{552} x& = & 85 \\\Leftrightarrow & x = \frac{85}{552} & & \\ & V = \left\{ \frac{85}{552} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{-120} \\\Leftrightarrow & 1320x+550x& = & 33-120 \\\Leftrightarrow & \color{red}{1870} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{1870} & & \\ & V = \left\{ \frac{-87}{1870} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{-297x} +15 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{+220} \\\Leftrightarrow & 660x+297x& = & 15+220 \\\Leftrightarrow & \color{red}{957} x& = & 235 \\\Leftrightarrow & x = \frac{235}{957} & & \\ & V = \left\{ \frac{235}{957} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{405x} +50 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-405x} & = & \color{red}{405x} +50 \color{blue}{-405x} \color{blue}{+36} \\\Leftrightarrow & -180x-405x& = & 50+36 \\\Leftrightarrow & \color{red}{-585} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-585} & & \\\Leftrightarrow & x = \frac{-86}{585} & & \\ & V = \left\{ \frac{-86}{585} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{7})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{-140x} +49 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +49 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & 336x+140x& = & 49+48 \\\Leftrightarrow & \color{red}{476} x& = & 97 \\\Leftrightarrow & x = \frac{97}{476} & & \\ & V = \left\{ \frac{97}{476} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{8})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{15}{8}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{400}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{280x} +48 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{-280x} & = & \color{red}{280x} +48 \color{blue}{-280x} \color{blue}{-75} \\\Leftrightarrow & 400x-280x& = & 48-75 \\\Leftrightarrow & \color{red}{120} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{120} & & \\\Leftrightarrow & x = \frac{-9}{40} & & \\ & V = \left\{ \frac{-9}{40} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-216} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 1350x \color{red}{-216} \color{blue}{+216} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+216} \\\Leftrightarrow & 1350x+315x& = & 50+216 \\\Leftrightarrow & \color{red}{1665} x& = & 266 \\\Leftrightarrow & x = \frac{266}{1665} & & \\ & V = \left\{ \frac{266}{1665} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 16x-\frac{8}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{105x} +25 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{+24} \\\Leftrightarrow & 240x-105x& = & 25+24 \\\Leftrightarrow & \color{red}{135} x& = & 49 \\\Leftrightarrow & x = \frac{49}{135} & & \\ & V = \left\{ \frac{49}{135} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{360}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 360x \color{red}{-72} & = & \color{red}{-150x} +35 \\\Leftrightarrow & 360x \color{red}{-72} \color{blue}{+72} \color{blue}{+150x} & = & \color{red}{-150x} +35 \color{blue}{+150x} \color{blue}{+72} \\\Leftrightarrow & 360x+150x& = & 35+72 \\\Leftrightarrow & \color{red}{510} x& = & 107 \\\Leftrightarrow & x = \frac{107}{510} & & \\ & V = \left\{ \frac{107}{510} \right\} & \\\end{align}\)
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