Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{-24} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -224x \color{red}{-24} \color{blue}{+24} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{+24} \\\Leftrightarrow & -224x+252x& = & 21+24 \\\Leftrightarrow & \color{red}{28} x& = & 45 \\\Leftrightarrow & x = \frac{45}{28} & & \\ & V = \left\{ \frac{45}{28} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+90} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1650x \color{red}{+90} \color{blue}{-90} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-90} \\\Leftrightarrow & -1650x-385x& = & 66-90 \\\Leftrightarrow & \color{red}{-2035} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-2035} & & \\\Leftrightarrow & x = \frac{24}{2035} & & \\ & V = \left\{ \frac{24}{2035} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{16}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+48} & = & \color{red}{231x} +88 \\\Leftrightarrow & 660x \color{red}{+48} \color{blue}{-48} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-48} \\\Leftrightarrow & 660x-231x& = & 88-48 \\\Leftrightarrow & \color{red}{429} x& = & 40 \\\Leftrightarrow & x = \frac{40}{429} & & \\ & V = \left\{ \frac{40}{429} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & -132x+55x& = & 2-24 \\\Leftrightarrow & \color{red}{-77} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-77} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-24} & = & \color{red}{-45x} +8 \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{+24} \\\Leftrightarrow & -36x+45x& = & 8+24 \\\Leftrightarrow & \color{red}{9} x& = & 32 \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+96} & = & \color{red}{-378x} +49 \\\Leftrightarrow & -336x \color{red}{+96} \color{blue}{-96} \color{blue}{+378x} & = & \color{red}{-378x} +49 \color{blue}{+378x} \color{blue}{-96} \\\Leftrightarrow & -336x+378x& = & 49-96 \\\Leftrightarrow & \color{red}{42} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{42} & & \\ & V = \left\{ \frac{-47}{42} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{-308} & = & \color{red}{-495x} +72 \\\Leftrightarrow & 2772x \color{red}{-308} \color{blue}{+308} \color{blue}{+495x} & = & \color{red}{-495x} +72 \color{blue}{+495x} \color{blue}{+308} \\\Leftrightarrow & 2772x+495x& = & 72+308 \\\Leftrightarrow & \color{red}{3267} x& = & 380 \\\Leftrightarrow & x = \frac{380}{3267} & & \\ & V = \left\{ \frac{380}{3267} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-72} \\\Leftrightarrow & -450x+105x& = & 10-72 \\\Leftrightarrow & \color{red}{-345} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-345} & & \\\Leftrightarrow & x = \frac{62}{345} & & \\ & V = \left\{ \frac{62}{345} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & -8x+\frac{5}{11} \\\Leftrightarrow & 21x+\frac{21}{11}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 231x \color{red}{+21} & = & \color{red}{-88x} +5 \\\Leftrightarrow & 231x \color{red}{+21} \color{blue}{-21} \color{blue}{+88x} & = & \color{red}{-88x} +5 \color{blue}{+88x} \color{blue}{-21} \\\Leftrightarrow & 231x+88x& = & 5-21 \\\Leftrightarrow & \color{red}{319} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{319} & & \\ & V = \left\{ \frac{-16}{319} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-105} & = & \color{red}{154x} +88 \\\Leftrightarrow & 1155x \color{red}{-105} \color{blue}{+105} \color{blue}{-154x} & = & \color{red}{154x} +88 \color{blue}{-154x} \color{blue}{+105} \\\Leftrightarrow & 1155x-154x& = & 88+105 \\\Leftrightarrow & \color{red}{1001} x& = & 193 \\\Leftrightarrow & x = \frac{193}{1001} & & \\ & V = \left\{ \frac{193}{1001} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{5})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-48} & = & \color{red}{140x} +35 \\\Leftrightarrow & 300x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & 300x-140x& = & 35+48 \\\Leftrightarrow & \color{red}{160} x& = & 83 \\\Leftrightarrow & x = \frac{83}{160} & & \\ & V = \left\{ \frac{83}{160} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{175x} +40 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 630x-175x& = & 40+84 \\\Leftrightarrow & \color{red}{455} x& = & 124 \\\Leftrightarrow & x = \frac{124}{455} & & \\ & V = \left\{ \frac{124}{455} \right\} & \\\end{align}\)
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