Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{35x} +2 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 60x-35x& = & 2+12 \\\Leftrightarrow & \color{red}{25} x& = & 14 \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{+100} & = & \color{red}{245x} +14 \\\Leftrightarrow & -560x \color{red}{+100} \color{blue}{-100} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-100} \\\Leftrightarrow & -560x-245x& = & 14-100 \\\Leftrightarrow & \color{red}{-805} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-805} & & \\\Leftrightarrow & x = \frac{86}{805} & & \\ & V = \left\{ \frac{86}{805} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{140x} +32 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +32 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & -400x-140x& = & 32+75 \\\Leftrightarrow & \color{red}{-540} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-540} & & \\\Leftrightarrow & x = \frac{-107}{540} & & \\ & V = \left\{ \frac{-107}{540} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 840x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 840x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{665} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{665} & & \\ & V = \left\{ \frac{-74}{665} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{5})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 35x+\frac{28}{5}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x+ \frac{308}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{+308} & = & \color{red}{110x} +10 \\\Leftrightarrow & 1925x \color{red}{+308} \color{blue}{-308} \color{blue}{-110x} & = & \color{red}{110x} +10 \color{blue}{-110x} \color{blue}{-308} \\\Leftrightarrow & 1925x-110x& = & 10-308 \\\Leftrightarrow & \color{red}{1815} x& = & -298 \\\Leftrightarrow & x = \frac{-298}{1815} & & \\ & V = \left\{ \frac{-298}{1815} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{12})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{25}{12}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-840}{ \color{blue}{84} }x- \frac{175}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{-588x} +48 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{+588x} & = & \color{red}{-588x} +48 \color{blue}{+588x} \color{blue}{+175} \\\Leftrightarrow & -840x+588x& = & 48+175 \\\Leftrightarrow & \color{red}{-252} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-252} & & \\\Leftrightarrow & x = \frac{-223}{252} & & \\ & V = \left\{ \frac{-223}{252} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{176x} +24 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{-176x} & = & \color{red}{176x} +24 \color{blue}{-176x} \color{blue}{+165} \\\Leftrightarrow & -660x-176x& = & 24+165 \\\Leftrightarrow & \color{red}{-836} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-836} & & \\\Leftrightarrow & x = \frac{-189}{836} & & \\ & V = \left\{ \frac{-189}{836} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{8})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{25}{8}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-400}{ \color{blue}{40} }x+ \frac{125}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -400x \color{red}{+125} & = & \color{red}{-280x} +12 \\\Leftrightarrow & -400x \color{red}{+125} \color{blue}{-125} \color{blue}{+280x} & = & \color{red}{-280x} +12 \color{blue}{+280x} \color{blue}{-125} \\\Leftrightarrow & -400x+280x& = & 12-125 \\\Leftrightarrow & \color{red}{-120} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-120} & & \\\Leftrightarrow & x = \frac{113}{120} & & \\ & V = \left\{ \frac{113}{120} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 4x+\frac{7}{9} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 4x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{180}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-54} & = & \color{red}{180x} +35 \\\Leftrightarrow & -675x \color{red}{-54} \color{blue}{+54} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{+54} \\\Leftrightarrow & -675x-180x& = & 35+54 \\\Leftrightarrow & \color{red}{-855} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-855} & & \\\Leftrightarrow & x = \frac{-89}{855} & & \\ & V = \left\{ \frac{-89}{855} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-72}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{+135} & = & \color{red}{-72x} +40 \\\Leftrightarrow & 324x \color{red}{+135} \color{blue}{-135} \color{blue}{+72x} & = & \color{red}{-72x} +40 \color{blue}{+72x} \color{blue}{-135} \\\Leftrightarrow & 324x+72x& = & 40-135 \\\Leftrightarrow & \color{red}{396} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{396} & & \\ & V = \left\{ \frac{-95}{396} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{320}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 320x \color{red}{+48} & = & \color{red}{-100x} +35 \\\Leftrightarrow & 320x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +35 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & 320x+100x& = & 35-48 \\\Leftrightarrow & \color{red}{420} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{420} & & \\ & V = \left\{ \frac{-13}{420} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{308x} +99 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{-120} \\\Leftrightarrow & -1320x-308x& = & 99-120 \\\Leftrightarrow & \color{red}{-1628} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-1628} & & \\\Leftrightarrow & x = \frac{21}{1628} & & \\ & V = \left\{ \frac{21}{1628} \right\} & \\\end{align}\)
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