Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{8})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -20x-\frac{15}{8}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{56}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{-45} & = & \color{red}{168x} +56 \\\Leftrightarrow & -480x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +56 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & -480x-168x& = & 56+45 \\\Leftrightarrow & \color{red}{-648} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-648} & & \\\Leftrightarrow & x = \frac{-101}{648} & & \\ & V = \left\{ \frac{-101}{648} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 15x+\frac{10}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+10} & = & \color{red}{49x} +6 \\\Leftrightarrow & 105x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & 105x-49x& = & 6-10 \\\Leftrightarrow & \color{red}{56} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{56} & & \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{5})& = & 4x+\frac{3}{4} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{700}{ \color{blue}{20} }x- \frac{56}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 700x \color{red}{-56} & = & \color{red}{80x} +15 \\\Leftrightarrow & 700x \color{red}{-56} \color{blue}{+56} \color{blue}{-80x} & = & \color{red}{80x} +15 \color{blue}{-80x} \color{blue}{+56} \\\Leftrightarrow & 700x-80x& = & 15+56 \\\Leftrightarrow & \color{red}{620} x& = & 71 \\\Leftrightarrow & x = \frac{71}{620} & & \\ & V = \left\{ \frac{71}{620} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 30-132 \\\Leftrightarrow & \color{red}{-935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-935} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{99x} +22 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{-99x} & = & \color{red}{99x} +22 \color{blue}{-99x} \color{blue}{-30} \\\Leftrightarrow & 330x-99x& = & 22-30 \\\Leftrightarrow & \color{red}{231} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{231} & & \\ & V = \left\{ \frac{-8}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{8})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{15}{8}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{720}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 720x \color{red}{-135} & = & \color{red}{504x} +64 \\\Leftrightarrow & 720x \color{red}{-135} \color{blue}{+135} \color{blue}{-504x} & = & \color{red}{504x} +64 \color{blue}{-504x} \color{blue}{+135} \\\Leftrightarrow & 720x-504x& = & 64+135 \\\Leftrightarrow & \color{red}{216} x& = & 199 \\\Leftrightarrow & x = \frac{199}{216} & & \\ & V = \left\{ \frac{199}{216} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{9})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 4x-\frac{4}{9}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{72}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{126x} +27 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{-126x} & = & \color{red}{126x} +27 \color{blue}{-126x} \color{blue}{+8} \\\Leftrightarrow & 72x-126x& = & 27+8 \\\Leftrightarrow & \color{red}{-54} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-54} & & \\\Leftrightarrow & x = \frac{-35}{54} & & \\ & V = \left\{ \frac{-35}{54} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -28x+\frac{35}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{+35} & = & \color{red}{-44x} +6 \\\Leftrightarrow & -308x \color{red}{+35} \color{blue}{-35} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{-35} \\\Leftrightarrow & -308x+44x& = & 6-35 \\\Leftrightarrow & \color{red}{-264} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-264} & & \\\Leftrightarrow & x = \frac{29}{264} & & \\ & V = \left\{ \frac{29}{264} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-75} & = & \color{red}{-40x} +8 \\\Leftrightarrow & 180x \color{red}{-75} \color{blue}{+75} \color{blue}{+40x} & = & \color{red}{-40x} +8 \color{blue}{+40x} \color{blue}{+75} \\\Leftrightarrow & 180x+40x& = & 8+75 \\\Leftrightarrow & \color{red}{220} x& = & 83 \\\Leftrightarrow & x = \frac{83}{220} & & \\ & V = \left\{ \frac{83}{220} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+10} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -28x \color{red}{+10} \color{blue}{-10} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-10} \\\Leftrightarrow & -28x+35x& = & 9-10 \\\Leftrightarrow & \color{red}{7} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{8})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{+189} & = & \color{red}{-216x} +64 \\\Leftrightarrow & 1008x \color{red}{+189} \color{blue}{-189} \color{blue}{+216x} & = & \color{red}{-216x} +64 \color{blue}{+216x} \color{blue}{-189} \\\Leftrightarrow & 1008x+216x& = & 64-189 \\\Leftrightarrow & \color{red}{1224} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1224} & & \\ & V = \left\{ \frac{-125}{1224} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{12})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2640}{ \color{blue}{132} }x+ \frac{275}{ \color{blue}{132} })& = & (\frac{-396}{ \color{blue}{132} }x+ \frac{96}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2640x \color{red}{+275} & = & \color{red}{-396x} +96 \\\Leftrightarrow & 2640x \color{red}{+275} \color{blue}{-275} \color{blue}{+396x} & = & \color{red}{-396x} +96 \color{blue}{+396x} \color{blue}{-275} \\\Leftrightarrow & 2640x+396x& = & 96-275 \\\Leftrightarrow & \color{red}{3036} x& = & -179 \\\Leftrightarrow & x = \frac{-179}{3036} & & \\ & V = \left\{ \frac{-179}{3036} \right\} & \\\end{align}\)
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