Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{2})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{35}{2}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-28}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{6}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -28x \color{red}{-35} & = & \color{red}{6x} +9 \\\Leftrightarrow & -28x \color{red}{-35} \color{blue}{+35} \color{blue}{-6x} & = & \color{red}{6x} +9 \color{blue}{-6x} \color{blue}{+35} \\\Leftrightarrow & -28x-6x& = & 9+35 \\\Leftrightarrow & \color{red}{-34} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-34} & & \\\Leftrightarrow & x = \frac{-22}{17} & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+18} & = & \color{red}{231x} +110 \\\Leftrightarrow & 330x \color{red}{+18} \color{blue}{-18} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-18} \\\Leftrightarrow & 330x-231x& = & 110-18 \\\Leftrightarrow & \color{red}{99} x& = & 92 \\\Leftrightarrow & x = \frac{92}{99} & & \\ & V = \left\{ \frac{92}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{11})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 14x-\frac{21}{11}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{105}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-105} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 770x \color{red}{-105} \color{blue}{+105} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+105} \\\Leftrightarrow & 770x+165x& = & 22+105 \\\Leftrightarrow & \color{red}{935} x& = & 127 \\\Leftrightarrow & x = \frac{127}{935} & & \\ & V = \left\{ \frac{127}{935} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+90} & = & \color{red}{297x} +110 \\\Leftrightarrow & 792x \color{red}{+90} \color{blue}{-90} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{-90} \\\Leftrightarrow & 792x-297x& = & 110-90 \\\Leftrightarrow & \color{red}{495} x& = & 20 \\\Leftrightarrow & x = \frac{20}{495} & & \\\Leftrightarrow & x = \frac{4}{99} & & \\ & V = \left\{ \frac{4}{99} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{-140x} +40 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +40 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & -252x+140x& = & 40+105 \\\Leftrightarrow & \color{red}{-112} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-112} & & \\\Leftrightarrow & x = \frac{-145}{112} & & \\ & V = \left\{ \frac{-145}{112} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-50x} +35 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{-12} \\\Leftrightarrow & -90x+50x& = & 35-12 \\\Leftrightarrow & \color{red}{-40} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-40} & & \\\Leftrightarrow & x = \frac{-23}{40} & & \\ & V = \left\{ \frac{-23}{40} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+12} & = & \color{red}{35x} +2 \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -30x-35x& = & 2-12 \\\Leftrightarrow & \color{red}{-65} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-65} & & \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 270x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{195} x& = & 4 \\\Leftrightarrow & x = \frac{4}{195} & & \\ & V = \left\{ \frac{4}{195} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-112} & = & \color{red}{-96x} +27 \\\Leftrightarrow & -252x \color{red}{-112} \color{blue}{+112} \color{blue}{+96x} & = & \color{red}{-96x} +27 \color{blue}{+96x} \color{blue}{+112} \\\Leftrightarrow & -252x+96x& = & 27+112 \\\Leftrightarrow & \color{red}{-156} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-156} & & \\\Leftrightarrow & x = \frac{-139}{156} & & \\ & V = \left\{ \frac{-139}{156} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 396x+165x& = & 88-36 \\\Leftrightarrow & \color{red}{561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{561} & & \\ & V = \left\{ \frac{52}{561} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{+108} & = & \color{red}{315x} +20 \\\Leftrightarrow & -720x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & -720x-315x& = & 20-108 \\\Leftrightarrow & \color{red}{-1035} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-1035} & & \\\Leftrightarrow & x = \frac{88}{1035} & & \\ & V = \left\{ \frac{88}{1035} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{2})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -15x-\frac{9}{2}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-63} & = & \color{red}{-56x} +8 \\\Leftrightarrow & -210x \color{red}{-63} \color{blue}{+63} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{+63} \\\Leftrightarrow & -210x+56x& = & 8+63 \\\Leftrightarrow & \color{red}{-154} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-154} & & \\\Leftrightarrow & x = \frac{-71}{154} & & \\ & V = \left\{ \frac{-71}{154} \right\} & \\\end{align}\)
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