Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{7})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1400}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1400x \color{red}{-200} & = & \color{red}{-210x} +63 \\\Leftrightarrow & -1400x \color{red}{-200} \color{blue}{+200} \color{blue}{+210x} & = & \color{red}{-210x} +63 \color{blue}{+210x} \color{blue}{+200} \\\Leftrightarrow & -1400x+210x& = & 63+200 \\\Leftrightarrow & \color{red}{-1190} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-1190} & & \\\Leftrightarrow & x = \frac{-263}{1190} & & \\ & V = \left\{ \frac{-263}{1190} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+132} & = & \color{red}{-385x} +56 \\\Leftrightarrow & 924x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 924x+385x& = & 56-132 \\\Leftrightarrow & \color{red}{1309} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{1309} & & \\ & V = \left\{ \frac{-76}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{-12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & 100x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 100x+35x& = & 7+12 \\\Leftrightarrow & \color{red}{135} x& = & 19 \\\Leftrightarrow & x = \frac{19}{135} & & \\ & V = \left\{ \frac{19}{135} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{2})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{21}{2}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-350}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -350x \color{red}{-105} & = & \color{red}{30x} +12 \\\Leftrightarrow & -350x \color{red}{-105} \color{blue}{+105} \color{blue}{-30x} & = & \color{red}{30x} +12 \color{blue}{-30x} \color{blue}{+105} \\\Leftrightarrow & -350x-30x& = & 12+105 \\\Leftrightarrow & \color{red}{-380} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-380} & & \\\Leftrightarrow & x = \frac{-117}{380} & & \\ & V = \left\{ \frac{-117}{380} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{-189x} +27 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & 84x+189x& = & 27+56 \\\Leftrightarrow & \color{red}{273} x& = & 83 \\\Leftrightarrow & x = \frac{83}{273} & & \\ & V = \left\{ \frac{83}{273} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 30x-\frac{12}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{-108} & = & \color{red}{693x} +88 \\\Leftrightarrow & 2970x \color{red}{-108} \color{blue}{+108} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+108} \\\Leftrightarrow & 2970x-693x& = & 88+108 \\\Leftrightarrow & \color{red}{2277} x& = & 196 \\\Leftrightarrow & x = \frac{196}{2277} & & \\ & V = \left\{ \frac{196}{2277} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+50} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 140x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & 140x+105x& = & 42-50 \\\Leftrightarrow & \color{red}{245} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{245} & & \\ & V = \left\{ \frac{-8}{245} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +20 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 20+132 \\\Leftrightarrow & \color{red}{-385} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-385} & & \\\Leftrightarrow & x = \frac{-152}{385} & & \\ & V = \left\{ \frac{-152}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 4x+\frac{3}{10} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{630}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{280}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 630x \color{red}{-60} & = & \color{red}{280x} +21 \\\Leftrightarrow & 630x \color{red}{-60} \color{blue}{+60} \color{blue}{-280x} & = & \color{red}{280x} +21 \color{blue}{-280x} \color{blue}{+60} \\\Leftrightarrow & 630x-280x& = & 21+60 \\\Leftrightarrow & \color{red}{350} x& = & 81 \\\Leftrightarrow & x = \frac{81}{350} & & \\ & V = \left\{ \frac{81}{350} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+32} & = & \color{red}{36x} +27 \\\Leftrightarrow & 120x \color{red}{+32} \color{blue}{-32} \color{blue}{-36x} & = & \color{red}{36x} +27 \color{blue}{-36x} \color{blue}{-32} \\\Leftrightarrow & 120x-36x& = & 27-32 \\\Leftrightarrow & \color{red}{84} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{84} & & \\ & V = \left\{ \frac{-5}{84} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 30x+\frac{24}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+24} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 330x \color{red}{+24} \color{blue}{-24} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-24} \\\Leftrightarrow & 330x+77x& = & 2-24 \\\Leftrightarrow & \color{red}{407} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{407} & & \\\Leftrightarrow & x = \frac{-2}{37} & & \\ & V = \left\{ \frac{-2}{37} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+18} & = & \color{red}{-20x} +15 \\\Leftrightarrow & 90x \color{red}{+18} \color{blue}{-18} \color{blue}{+20x} & = & \color{red}{-20x} +15 \color{blue}{+20x} \color{blue}{-18} \\\Leftrightarrow & 90x+20x& = & 15-18 \\\Leftrightarrow & \color{red}{110} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{110} & & \\ & V = \left\{ \frac{-3}{110} \right\} & \\\end{align}\)
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