Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & 2310x+539x& = & 66-126 \\\Leftrightarrow & \color{red}{2849} x& = & -60 \\\Leftrightarrow & x = \frac{-60}{2849} & & \\ & V = \left\{ \frac{-60}{2849} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{105x} +10 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-12} \\\Leftrightarrow & -90x-105x& = & 10-12 \\\Leftrightarrow & \color{red}{-195} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-195} & & \\\Leftrightarrow & x = \frac{2}{195} & & \\ & V = \left\{ \frac{2}{195} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & 9x+\frac{7}{9} \\\Leftrightarrow & -4x-\frac{6}{5}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-54} & = & \color{red}{405x} +35 \\\Leftrightarrow & -180x \color{red}{-54} \color{blue}{+54} \color{blue}{-405x} & = & \color{red}{405x} +35 \color{blue}{-405x} \color{blue}{+54} \\\Leftrightarrow & -180x-405x& = & 35+54 \\\Leftrightarrow & \color{red}{-585} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-585} & & \\\Leftrightarrow & x = \frac{-89}{585} & & \\ & V = \left\{ \frac{-89}{585} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 990x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 990x+275x& = & 20-264 \\\Leftrightarrow & \color{red}{1265} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{1265} & & \\ & V = \left\{ \frac{-244}{1265} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{4}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+44} & = & \color{red}{-297x} +54 \\\Leftrightarrow & 990x \color{red}{+44} \color{blue}{-44} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-44} \\\Leftrightarrow & 990x+297x& = & 54-44 \\\Leftrightarrow & \color{red}{1287} x& = & 10 \\\Leftrightarrow & x = \frac{10}{1287} & & \\ & V = \left\{ \frac{10}{1287} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+20} & = & \color{red}{-28x} +8 \\\Leftrightarrow & -175x \color{red}{+20} \color{blue}{-20} \color{blue}{+28x} & = & \color{red}{-28x} +8 \color{blue}{+28x} \color{blue}{-20} \\\Leftrightarrow & -175x+28x& = & 8-20 \\\Leftrightarrow & \color{red}{-147} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-147} & & \\\Leftrightarrow & x = \frac{4}{49} & & \\ & V = \left\{ \frac{4}{49} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-28} & = & \color{red}{18x} +15 \\\Leftrightarrow & 168x \color{red}{-28} \color{blue}{+28} \color{blue}{-18x} & = & \color{red}{18x} +15 \color{blue}{-18x} \color{blue}{+28} \\\Leftrightarrow & 168x-18x& = & 15+28 \\\Leftrightarrow & \color{red}{150} x& = & 43 \\\Leftrightarrow & x = \frac{43}{150} & & \\ & V = \left\{ \frac{43}{150} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{8}{9}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{90x} +45 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{+16} \\\Leftrightarrow & -72x-90x& = & 45+16 \\\Leftrightarrow & \color{red}{-162} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-162} & & \\\Leftrightarrow & x = \frac{-61}{162} & & \\ & V = \left\{ \frac{-61}{162} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{2})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{15}{2}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{250}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 250x \color{red}{+75} & = & \color{red}{-80x} +12 \\\Leftrightarrow & 250x \color{red}{+75} \color{blue}{-75} \color{blue}{+80x} & = & \color{red}{-80x} +12 \color{blue}{+80x} \color{blue}{-75} \\\Leftrightarrow & 250x+80x& = & 12-75 \\\Leftrightarrow & \color{red}{330} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{330} & & \\\Leftrightarrow & x = \frac{-21}{110} & & \\ & V = \left\{ \frac{-21}{110} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{-48} \\\Leftrightarrow & 396x+110x& = & 99-48 \\\Leftrightarrow & \color{red}{506} x& = & 51 \\\Leftrightarrow & x = \frac{51}{506} & & \\ & V = \left\{ \frac{51}{506} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{105x} +9 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +9 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & -252x-105x& = & 9-56 \\\Leftrightarrow & \color{red}{-357} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-357} & & \\\Leftrightarrow & x = \frac{47}{357} & & \\ & V = \left\{ \frac{47}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -35x-\frac{14}{11}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x- \frac{140}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{-140} & = & \color{red}{330x} +99 \\\Leftrightarrow & -3850x \color{red}{-140} \color{blue}{+140} \color{blue}{-330x} & = & \color{red}{330x} +99 \color{blue}{-330x} \color{blue}{+140} \\\Leftrightarrow & -3850x-330x& = & 99+140 \\\Leftrightarrow & \color{red}{-4180} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-4180} & & \\\Leftrightarrow & x = \frac{-239}{4180} & & \\ & V = \left\{ \frac{-239}{4180} \right\} & \\\end{align}\)
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