Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{16}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+48} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{+48} \color{blue}{-48} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-48} \\\Leftrightarrow & -396x-165x& = & 88-48 \\\Leftrightarrow & \color{red}{-561} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-561} & & \\\Leftrightarrow & x = \frac{-40}{561} & & \\ & V = \left\{ \frac{-40}{561} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{24}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-120} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{-120} \color{blue}{+120} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+120} \\\Leftrightarrow & -1650x+385x& = & 66+120 \\\Leftrightarrow & \color{red}{-1265} x& = & 186 \\\Leftrightarrow & x = \frac{186}{-1265} & & \\\Leftrightarrow & x = \frac{-186}{1265} & & \\ & V = \left\{ \frac{-186}{1265} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{240}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+240} & = & \color{red}{550x} +33 \\\Leftrightarrow & -1320x \color{red}{+240} \color{blue}{-240} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{-240} \\\Leftrightarrow & -1320x-550x& = & 33-240 \\\Leftrightarrow & \color{red}{-1870} x& = & -207 \\\Leftrightarrow & x = \frac{-207}{-1870} & & \\\Leftrightarrow & x = \frac{207}{1870} & & \\ & V = \left\{ \frac{207}{1870} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-12} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 140x \color{red}{-12} \color{blue}{+12} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+12} \\\Leftrightarrow & 140x+98x& = & 49+12 \\\Leftrightarrow & \color{red}{238} x& = & 61 \\\Leftrightarrow & x = \frac{61}{238} & & \\ & V = \left\{ \frac{61}{238} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -28x-\frac{35}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-385} & = & \color{red}{693x} +54 \\\Leftrightarrow & -2772x \color{red}{-385} \color{blue}{+385} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+385} \\\Leftrightarrow & -2772x-693x& = & 54+385 \\\Leftrightarrow & \color{red}{-3465} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-3465} & & \\\Leftrightarrow & x = \frac{-439}{3465} & & \\ & V = \left\{ \frac{-439}{3465} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 6x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{336}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{+147} & = & \color{red}{336x} +80 \\\Leftrightarrow & 1960x \color{red}{+147} \color{blue}{-147} \color{blue}{-336x} & = & \color{red}{336x} +80 \color{blue}{-336x} \color{blue}{-147} \\\Leftrightarrow & 1960x-336x& = & 80-147 \\\Leftrightarrow & \color{red}{1624} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{1624} & & \\ & V = \left\{ \frac{-67}{1624} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-135} & = & \color{red}{693x} +77 \\\Leftrightarrow & -990x \color{red}{-135} \color{blue}{+135} \color{blue}{-693x} & = & \color{red}{693x} +77 \color{blue}{-693x} \color{blue}{+135} \\\Leftrightarrow & -990x-693x& = & 77+135 \\\Leftrightarrow & \color{red}{-1683} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-1683} & & \\\Leftrightarrow & x = \frac{-212}{1683} & & \\ & V = \left\{ \frac{-212}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{-75x} +6 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{+75x} & = & \color{red}{-75x} +6 \color{blue}{+75x} \color{blue}{+40} \\\Leftrightarrow & -180x+75x& = & 6+40 \\\Leftrightarrow & \color{red}{-105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-105} & & \\\Leftrightarrow & x = \frac{-46}{105} & & \\ & V = \left\{ \frac{-46}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -8x+\frac{8}{7} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{-6} & = & \color{red}{-56x} +8 \\\Leftrightarrow & 63x \color{red}{-6} \color{blue}{+6} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{+6} \\\Leftrightarrow & 63x+56x& = & 8+6 \\\Leftrightarrow & \color{red}{119} x& = & 14 \\\Leftrightarrow & x = \frac{14}{119} & & \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{25}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{75}{ \color{blue}{3} }x+ \frac{25}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 75x \color{red}{+25} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 75x \color{red}{+25} \color{blue}{-25} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-25} \\\Leftrightarrow & 75x+21x& = & 10-25 \\\Leftrightarrow & \color{red}{96} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{96} & & \\\Leftrightarrow & x = \frac{-5}{32} & & \\ & V = \left\{ \frac{-5}{32} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+8} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -100x \color{red}{+8} \color{blue}{-8} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-8} \\\Leftrightarrow & -100x+70x& = & 3-8 \\\Leftrightarrow & \color{red}{-30} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-30} & & \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+40} & = & \color{red}{-105x} +24 \\\Leftrightarrow & -300x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & -300x+105x& = & 24-40 \\\Leftrightarrow & \color{red}{-195} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-195} & & \\\Leftrightarrow & x = \frac{16}{195} & & \\ & V = \left\{ \frac{16}{195} \right\} & \\\end{align}\)
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