Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-50x} +25 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -120x+50x& = & 25+24 \\\Leftrightarrow & \color{red}{-70} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-70} & & \\\Leftrightarrow & x = \frac{-7}{10} & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{2})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -9x-\frac{9}{2}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-18}{ \color{blue}{2} }x- \frac{9}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -18x \color{red}{-9} & = & \color{red}{-10x} +9 \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{+10x} & = & \color{red}{-10x} +9 \color{blue}{+10x} \color{blue}{+9} \\\Leftrightarrow & -18x+10x& = & 9+9 \\\Leftrightarrow & \color{red}{-8} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-8} & & \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -16x+\frac{16}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{176}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+176} & = & \color{red}{385x} +30 \\\Leftrightarrow & -880x \color{red}{+176} \color{blue}{-176} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-176} \\\Leftrightarrow & -880x-385x& = & 30-176 \\\Leftrightarrow & \color{red}{-1265} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{-1265} & & \\\Leftrightarrow & x = \frac{146}{1265} & & \\ & V = \left\{ \frac{146}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{3})& = & 8x+\frac{9}{10} \\\Leftrightarrow & 21x+\frac{35}{3}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x+ \frac{350}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{+350} & = & \color{red}{240x} +27 \\\Leftrightarrow & 630x \color{red}{+350} \color{blue}{-350} \color{blue}{-240x} & = & \color{red}{240x} +27 \color{blue}{-240x} \color{blue}{-350} \\\Leftrightarrow & 630x-240x& = & 27-350 \\\Leftrightarrow & \color{red}{390} x& = & -323 \\\Leftrightarrow & x = \frac{-323}{390} & & \\ & V = \left\{ \frac{-323}{390} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{320}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 320x \color{red}{+96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 320x \color{red}{+96} \color{blue}{-96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{-96} \\\Leftrightarrow & 320x+200x& = & 35-96 \\\Leftrightarrow & \color{red}{520} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{520} & & \\ & V = \left\{ \frac{-61}{520} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{7})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{25}{7}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{50}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-50} & = & \color{red}{-42x} +49 \\\Leftrightarrow & 280x \color{red}{-50} \color{blue}{+50} \color{blue}{+42x} & = & \color{red}{-42x} +49 \color{blue}{+42x} \color{blue}{+50} \\\Leftrightarrow & 280x+42x& = & 49+50 \\\Leftrightarrow & \color{red}{322} x& = & 99 \\\Leftrightarrow & x = \frac{99}{322} & & \\ & V = \left\{ \frac{99}{322} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{20}{3}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+220} & = & \color{red}{-264x} +6 \\\Leftrightarrow & -495x \color{red}{+220} \color{blue}{-220} \color{blue}{+264x} & = & \color{red}{-264x} +6 \color{blue}{+264x} \color{blue}{-220} \\\Leftrightarrow & -495x+264x& = & 6-220 \\\Leftrightarrow & \color{red}{-231} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-231} & & \\\Leftrightarrow & x = \frac{214}{231} & & \\ & V = \left\{ \frac{214}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-154} & = & \color{red}{-264x} +6 \\\Leftrightarrow & -693x \color{red}{-154} \color{blue}{+154} \color{blue}{+264x} & = & \color{red}{-264x} +6 \color{blue}{+264x} \color{blue}{+154} \\\Leftrightarrow & -693x+264x& = & 6+154 \\\Leftrightarrow & \color{red}{-429} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-429} & & \\\Leftrightarrow & x = \frac{-160}{429} & & \\ & V = \left\{ \frac{-160}{429} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -14x+\frac{28}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{+196} & = & \color{red}{-63x} +9 \\\Leftrightarrow & -294x \color{red}{+196} \color{blue}{-196} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{-196} \\\Leftrightarrow & -294x+63x& = & 9-196 \\\Leftrightarrow & \color{red}{-231} x& = & -187 \\\Leftrightarrow & x = \frac{-187}{-231} & & \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{+24} & = & \color{red}{27x} +2 \\\Leftrightarrow & 144x \color{red}{+24} \color{blue}{-24} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{-24} \\\Leftrightarrow & 144x-27x& = & 2-24 \\\Leftrightarrow & \color{red}{117} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{117} & & \\ & V = \left\{ \frac{-22}{117} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-80} & = & \color{red}{140x} +21 \\\Leftrightarrow & -336x \color{red}{-80} \color{blue}{+80} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{+80} \\\Leftrightarrow & -336x-140x& = & 21+80 \\\Leftrightarrow & \color{red}{-476} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-476} & & \\\Leftrightarrow & x = \frac{-101}{476} & & \\ & V = \left\{ \frac{-101}{476} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 25x-\frac{10}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{75}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 75x \color{red}{-10} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 75x \color{red}{-10} \color{blue}{+10} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+10} \\\Leftrightarrow & 75x+27x& = & 8+10 \\\Leftrightarrow & \color{red}{102} x& = & 18 \\\Leftrightarrow & x = \frac{18}{102} & & \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
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