Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{5})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 28x-\frac{28}{5}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-308} & = & \color{red}{165x} +25 \\\Leftrightarrow & 1540x \color{red}{-308} \color{blue}{+308} \color{blue}{-165x} & = & \color{red}{165x} +25 \color{blue}{-165x} \color{blue}{+308} \\\Leftrightarrow & 1540x-165x& = & 25+308 \\\Leftrightarrow & \color{red}{1375} x& = & 333 \\\Leftrightarrow & x = \frac{333}{1375} & & \\ & V = \left\{ \frac{333}{1375} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+154} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 462x \color{red}{+154} \color{blue}{-154} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-154} \\\Leftrightarrow & 462x+297x& = & 18-154 \\\Leftrightarrow & \color{red}{759} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{759} & & \\ & V = \left\{ \frac{-136}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{11})& = & 4x+\frac{9}{11} \\\Leftrightarrow & -25x-\frac{20}{11}& = & 4x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x- \frac{20}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{-20} & = & \color{red}{44x} +9 \\\Leftrightarrow & -275x \color{red}{-20} \color{blue}{+20} \color{blue}{-44x} & = & \color{red}{44x} +9 \color{blue}{-44x} \color{blue}{+20} \\\Leftrightarrow & -275x-44x& = & 9+20 \\\Leftrightarrow & \color{red}{-319} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-319} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-264} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 660x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & 660x+275x& = & 50+264 \\\Leftrightarrow & \color{red}{935} x& = & 314 \\\Leftrightarrow & x = \frac{314}{935} & & \\ & V = \left\{ \frac{314}{935} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+8} & = & \color{red}{-27x} +2 \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & -12x+27x& = & 2-8 \\\Leftrightarrow & \color{red}{15} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{15} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{4}{3}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{-12} \\\Leftrightarrow & -90x+63x& = & 8-12 \\\Leftrightarrow & \color{red}{-27} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-27} & & \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{8})& = & -8x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{35}{8}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x+ \frac{245}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{+245} & = & \color{red}{-448x} +48 \\\Leftrightarrow & 1176x \color{red}{+245} \color{blue}{-245} \color{blue}{+448x} & = & \color{red}{-448x} +48 \color{blue}{+448x} \color{blue}{-245} \\\Leftrightarrow & 1176x+448x& = & 48-245 \\\Leftrightarrow & \color{red}{1624} x& = & -197 \\\Leftrightarrow & x = \frac{-197}{1624} & & \\ & V = \left\{ \frac{-197}{1624} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-8} & = & \color{red}{50x} +25 \\\Leftrightarrow & 80x \color{red}{-8} \color{blue}{+8} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{+8} \\\Leftrightarrow & 80x-50x& = & 25+8 \\\Leftrightarrow & \color{red}{30} x& = & 33 \\\Leftrightarrow & x = \frac{33}{30} & & \\\Leftrightarrow & x = \frac{11}{10} & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{175x} +42 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & -315x-175x& = & 42+30 \\\Leftrightarrow & \color{red}{-490} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-490} & & \\\Leftrightarrow & x = \frac{-36}{245} & & \\ & V = \left\{ \frac{-36}{245} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{50x} +15 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+18} \\\Leftrightarrow & 60x-50x& = & 15+18 \\\Leftrightarrow & \color{red}{10} x& = & 33 \\\Leftrightarrow & x = \frac{33}{10} & & \\ & V = \left\{ \frac{33}{10} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -360x-105x& = & 50-36 \\\Leftrightarrow & \color{red}{-465} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-465} & & \\\Leftrightarrow & x = \frac{-14}{465} & & \\ & V = \left\{ \frac{-14}{465} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{4}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{12}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-12} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 168x \color{red}{-12} \color{blue}{+12} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+12} \\\Leftrightarrow & 168x+147x& = & 14+12 \\\Leftrightarrow & \color{red}{315} x& = & 26 \\\Leftrightarrow & x = \frac{26}{315} & & \\ & V = \left\{ \frac{26}{315} \right\} & \\\end{align}\)
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