Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{8}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-40} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -220x \color{red}{-40} \color{blue}{+40} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+40} \\\Leftrightarrow & -220x+275x& = & 66+40 \\\Leftrightarrow & \color{red}{55} x& = & 106 \\\Leftrightarrow & x = \frac{106}{55} & & \\ & V = \left\{ \frac{106}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -20x+\frac{15}{7}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+75} & = & \color{red}{-315x} +28 \\\Leftrightarrow & -700x \color{red}{+75} \color{blue}{-75} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{-75} \\\Leftrightarrow & -700x+315x& = & 28-75 \\\Leftrightarrow & \color{red}{-385} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-385} & & \\\Leftrightarrow & x = \frac{47}{385} & & \\ & V = \left\{ \frac{47}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+12} & = & \color{red}{70x} +35 \\\Leftrightarrow & 112x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & 112x-70x& = & 35-12 \\\Leftrightarrow & \color{red}{42} x& = & 23 \\\Leftrightarrow & x = \frac{23}{42} & & \\ & V = \left\{ \frac{23}{42} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{224}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+224} & = & \color{red}{-216x} +21 \\\Leftrightarrow & 336x \color{red}{+224} \color{blue}{-224} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{-224} \\\Leftrightarrow & 336x+216x& = & 21-224 \\\Leftrightarrow & \color{red}{552} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{552} & & \\ & V = \left\{ \frac{-203}{552} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{-135} & = & \color{red}{-252x} +32 \\\Leftrightarrow & 900x \color{red}{-135} \color{blue}{+135} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{+135} \\\Leftrightarrow & 900x+252x& = & 32+135 \\\Leftrightarrow & \color{red}{1152} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1152} & & \\ & V = \left\{ \frac{167}{1152} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & 8x+\frac{4}{11} \\\Leftrightarrow & 25x-\frac{10}{7}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-110} & = & \color{red}{616x} +28 \\\Leftrightarrow & 1925x \color{red}{-110} \color{blue}{+110} \color{blue}{-616x} & = & \color{red}{616x} +28 \color{blue}{-616x} \color{blue}{+110} \\\Leftrightarrow & 1925x-616x& = & 28+110 \\\Leftrightarrow & \color{red}{1309} x& = & 138 \\\Leftrightarrow & x = \frac{138}{1309} & & \\ & V = \left\{ \frac{138}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{8})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{35}{8}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{105}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+105} & = & \color{red}{96x} +32 \\\Leftrightarrow & -672x \color{red}{+105} \color{blue}{-105} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{-105} \\\Leftrightarrow & -672x-96x& = & 32-105 \\\Leftrightarrow & \color{red}{-768} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-768} & & \\\Leftrightarrow & x = \frac{73}{768} & & \\ & V = \left\{ \frac{73}{768} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{-165} & = & \color{red}{264x} +16 \\\Leftrightarrow & 1760x \color{red}{-165} \color{blue}{+165} \color{blue}{-264x} & = & \color{red}{264x} +16 \color{blue}{-264x} \color{blue}{+165} \\\Leftrightarrow & 1760x-264x& = & 16+165 \\\Leftrightarrow & \color{red}{1496} x& = & 181 \\\Leftrightarrow & x = \frac{181}{1496} & & \\ & V = \left\{ \frac{181}{1496} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{105x} +42 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 700x-105x& = & 42+100 \\\Leftrightarrow & \color{red}{595} x& = & 142 \\\Leftrightarrow & x = \frac{142}{595} & & \\ & V = \left\{ \frac{142}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{4}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{16}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-16} & = & \color{red}{308x} +33 \\\Leftrightarrow & -440x \color{red}{-16} \color{blue}{+16} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{+16} \\\Leftrightarrow & -440x-308x& = & 33+16 \\\Leftrightarrow & \color{red}{-748} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-748} & & \\\Leftrightarrow & x = \frac{-49}{748} & & \\ & V = \left\{ \frac{-49}{748} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{9})& = & 3x+\frac{7}{10} \\\Leftrightarrow & 10x+\frac{10}{9}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{900}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 900x \color{red}{+100} & = & \color{red}{270x} +63 \\\Leftrightarrow & 900x \color{red}{+100} \color{blue}{-100} \color{blue}{-270x} & = & \color{red}{270x} +63 \color{blue}{-270x} \color{blue}{-100} \\\Leftrightarrow & 900x-270x& = & 63-100 \\\Leftrightarrow & \color{red}{630} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{630} & & \\ & V = \left\{ \frac{-37}{630} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{11})& = & 3x+\frac{7}{10} \\\Leftrightarrow & -20x+\frac{20}{11}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{+200} & = & \color{red}{330x} +77 \\\Leftrightarrow & -2200x \color{red}{+200} \color{blue}{-200} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{-200} \\\Leftrightarrow & -2200x-330x& = & 77-200 \\\Leftrightarrow & \color{red}{-2530} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-2530} & & \\\Leftrightarrow & x = \frac{123}{2530} & & \\ & V = \left\{ \frac{123}{2530} \right\} & \\\end{align}\)
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