Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+40} & = & \color{red}{135x} +18 \\\Leftrightarrow & -120x \color{red}{+40} \color{blue}{-40} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{-40} \\\Leftrightarrow & -120x-135x& = & 18-40 \\\Leftrightarrow & \color{red}{-255} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-255} & & \\\Leftrightarrow & x = \frac{22}{255} & & \\ & V = \left\{ \frac{22}{255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-88} & = & \color{red}{231x} +30 \\\Leftrightarrow & -330x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & -330x-231x& = & 30+88 \\\Leftrightarrow & \color{red}{-561} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-561} & & \\\Leftrightarrow & x = \frac{-118}{561} & & \\ & V = \left\{ \frac{-118}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-270}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{20}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -270x \color{red}{-27} & = & \color{red}{-150x} +20 \\\Leftrightarrow & -270x \color{red}{-27} \color{blue}{+27} \color{blue}{+150x} & = & \color{red}{-150x} +20 \color{blue}{+150x} \color{blue}{+27} \\\Leftrightarrow & -270x+150x& = & 20+27 \\\Leftrightarrow & \color{red}{-120} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-120} & & \\\Leftrightarrow & x = \frac{-47}{120} & & \\ & V = \left\{ \frac{-47}{120} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{9})& = & -4x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{35}{9}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{-144}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{+140} & = & \color{red}{-144x} +27 \\\Leftrightarrow & 1260x \color{red}{+140} \color{blue}{-140} \color{blue}{+144x} & = & \color{red}{-144x} +27 \color{blue}{+144x} \color{blue}{-140} \\\Leftrightarrow & 1260x+144x& = & 27-140 \\\Leftrightarrow & \color{red}{1404} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{1404} & & \\ & V = \left\{ \frac{-113}{1404} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{6})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -10x-\frac{25}{6}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{-125} & = & \color{red}{210x} +9 \\\Leftrightarrow & -300x \color{red}{-125} \color{blue}{+125} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{+125} \\\Leftrightarrow & -300x-210x& = & 9+125 \\\Leftrightarrow & \color{red}{-510} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-510} & & \\\Leftrightarrow & x = \frac{-67}{255} & & \\ & V = \left\{ \frac{-67}{255} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -21x-\frac{35}{3}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-35} & = & \color{red}{-24x} +7 \\\Leftrightarrow & -63x \color{red}{-35} \color{blue}{+35} \color{blue}{+24x} & = & \color{red}{-24x} +7 \color{blue}{+24x} \color{blue}{+35} \\\Leftrightarrow & -63x+24x& = & 7+35 \\\Leftrightarrow & \color{red}{-39} x& = & 42 \\\Leftrightarrow & x = \frac{42}{-39} & & \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{200x} +45 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & 480x-200x& = & 45-96 \\\Leftrightarrow & \color{red}{280} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{280} & & \\ & V = \left\{ \frac{-51}{280} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+72} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -180x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -180x+75x& = & 40-72 \\\Leftrightarrow & \color{red}{-105} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-105} & & \\\Leftrightarrow & x = \frac{32}{105} & & \\ & V = \left\{ \frac{32}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & 3x+\frac{5}{7} \\\Leftrightarrow & 14x+\frac{21}{11}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{+147} & = & \color{red}{231x} +55 \\\Leftrightarrow & 1078x \color{red}{+147} \color{blue}{-147} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{-147} \\\Leftrightarrow & 1078x-231x& = & 55-147 \\\Leftrightarrow & \color{red}{847} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{847} & & \\ & V = \left\{ \frac{-92}{847} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{9})& = & -3x+\frac{3}{11} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+385} & = & \color{red}{-297x} +27 \\\Leftrightarrow & -1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+297x} & = & \color{red}{-297x} +27 \color{blue}{+297x} \color{blue}{-385} \\\Leftrightarrow & -1386x+297x& = & 27-385 \\\Leftrightarrow & \color{red}{-1089} x& = & -358 \\\Leftrightarrow & x = \frac{-358}{-1089} & & \\\Leftrightarrow & x = \frac{358}{1089} & & \\ & V = \left\{ \frac{358}{1089} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{-270} & = & \color{red}{315x} +14 \\\Leftrightarrow & 1512x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & 1512x-315x& = & 14+270 \\\Leftrightarrow & \color{red}{1197} x& = & 284 \\\Leftrightarrow & x = \frac{284}{1197} & & \\ & V = \left\{ \frac{284}{1197} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{55x} +10 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{-55x} & = & \color{red}{55x} +10 \color{blue}{-55x} \color{blue}{-30} \\\Leftrightarrow & 198x-55x& = & 10-30 \\\Leftrightarrow & \color{red}{143} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{143} & & \\ & V = \left\{ \frac{-20}{143} \right\} & \\\end{align}\)
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