Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{10}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+20} & = & \color{red}{-66x} +55 \\\Leftrightarrow & 176x \color{red}{+20} \color{blue}{-20} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{-20} \\\Leftrightarrow & 176x+66x& = & 55-20 \\\Leftrightarrow & \color{red}{242} x& = & 35 \\\Leftrightarrow & x = \frac{35}{242} & & \\ & V = \left\{ \frac{35}{242} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-30} & = & \color{red}{-245x} +49 \\\Leftrightarrow & -350x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +49 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & -350x+245x& = & 49+30 \\\Leftrightarrow & \color{red}{-105} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-105} & & \\\Leftrightarrow & x = \frac{-79}{105} & & \\ & V = \left\{ \frac{-79}{105} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{7})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -8x-\frac{10}{7}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-90} & = & \color{red}{-189x} +14 \\\Leftrightarrow & -504x \color{red}{-90} \color{blue}{+90} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{+90} \\\Leftrightarrow & -504x+189x& = & 14+90 \\\Leftrightarrow & \color{red}{-315} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-315} & & \\\Leftrightarrow & x = \frac{-104}{315} & & \\ & V = \left\{ \frac{-104}{315} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+6} & = & \color{red}{63x} +8 \\\Leftrightarrow & -56x \color{red}{+6} \color{blue}{-6} \color{blue}{-63x} & = & \color{red}{63x} +8 \color{blue}{-63x} \color{blue}{-6} \\\Leftrightarrow & -56x-63x& = & 8-6 \\\Leftrightarrow & \color{red}{-119} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-119} & & \\\Leftrightarrow & x = \frac{-2}{119} & & \\ & V = \left\{ \frac{-2}{119} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{8}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+24} \\\Leftrightarrow & -198x+231x& = & 88+24 \\\Leftrightarrow & \color{red}{33} x& = & 112 \\\Leftrightarrow & x = \frac{112}{33} & & \\ & V = \left\{ \frac{112}{33} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{315x} +35 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{+90} \\\Leftrightarrow & 378x-315x& = & 35+90 \\\Leftrightarrow & \color{red}{63} x& = & 125 \\\Leftrightarrow & x = \frac{125}{63} & & \\ & V = \left\{ \frac{125}{63} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 9x+\frac{9}{11} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-88} & = & \color{red}{891x} +81 \\\Leftrightarrow & 1584x \color{red}{-88} \color{blue}{+88} \color{blue}{-891x} & = & \color{red}{891x} +81 \color{blue}{-891x} \color{blue}{+88} \\\Leftrightarrow & 1584x-891x& = & 81+88 \\\Leftrightarrow & \color{red}{693} x& = & 169 \\\Leftrightarrow & x = \frac{169}{693} & & \\ & V = \left\{ \frac{169}{693} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 4x+\frac{10}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+50} & = & \color{red}{105x} +18 \\\Leftrightarrow & 60x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 60x-105x& = & 18-50 \\\Leftrightarrow & \color{red}{-45} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-45} & & \\\Leftrightarrow & x = \frac{32}{45} & & \\ & V = \left\{ \frac{32}{45} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{2})& = & 8x+\frac{3}{7} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 8x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+105} & = & \color{red}{112x} +6 \\\Leftrightarrow & -210x \color{red}{+105} \color{blue}{-105} \color{blue}{-112x} & = & \color{red}{112x} +6 \color{blue}{-112x} \color{blue}{-105} \\\Leftrightarrow & -210x-112x& = & 6-105 \\\Leftrightarrow & \color{red}{-322} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{-322} & & \\\Leftrightarrow & x = \frac{99}{322} & & \\ & V = \left\{ \frac{99}{322} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{3})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{10}{3}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{+10} & = & \color{red}{6x} +10 \\\Leftrightarrow & 45x \color{red}{+10} \color{blue}{-10} \color{blue}{-6x} & = & \color{red}{6x} +10 \color{blue}{-6x} \color{blue}{-10} \\\Leftrightarrow & 45x-6x& = & 10-10 \\\Leftrightarrow & \color{red}{39} x& = & 0 \\\Leftrightarrow & x = \frac{0}{39} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{11})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+8} & = & \color{red}{-99x} +8 \\\Leftrightarrow & -88x \color{red}{+8} \color{blue}{-8} \color{blue}{+99x} & = & \color{red}{-99x} +8 \color{blue}{+99x} \color{blue}{-8} \\\Leftrightarrow & -88x+99x& = & 8-8 \\\Leftrightarrow & \color{red}{11} x& = & 0 \\\Leftrightarrow & x = \frac{0}{11} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{396}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{330x} +77 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{-36} \\\Leftrightarrow & 396x-330x& = & 77-36 \\\Leftrightarrow & \color{red}{66} x& = & 41 \\\Leftrightarrow & x = \frac{41}{66} & & \\ & V = \left\{ \frac{41}{66} \right\} & \\\end{align}\)
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