Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -18x+\frac{18}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-50x} +25 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-36} \\\Leftrightarrow & -180x+50x& = & 25-36 \\\Leftrightarrow & \color{red}{-130} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-130} & & \\\Leftrightarrow & x = \frac{11}{130} & & \\ & V = \left\{ \frac{11}{130} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -14x-\frac{28}{3}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x- \frac{280}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{-280} & = & \color{red}{90x} +27 \\\Leftrightarrow & -420x \color{red}{-280} \color{blue}{+280} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{+280} \\\Leftrightarrow & -420x-90x& = & 27+280 \\\Leftrightarrow & \color{red}{-510} x& = & 307 \\\Leftrightarrow & x = \frac{307}{-510} & & \\\Leftrightarrow & x = \frac{-307}{510} & & \\ & V = \left\{ \frac{-307}{510} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 540x+225x& = & 50+108 \\\Leftrightarrow & \color{red}{765} x& = & 158 \\\Leftrightarrow & x = \frac{158}{765} & & \\ & V = \left\{ \frac{158}{765} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-80} & = & \color{red}{-150x} +27 \\\Leftrightarrow & 180x \color{red}{-80} \color{blue}{+80} \color{blue}{+150x} & = & \color{red}{-150x} +27 \color{blue}{+150x} \color{blue}{+80} \\\Leftrightarrow & 180x+150x& = & 27+80 \\\Leftrightarrow & \color{red}{330} x& = & 107 \\\Leftrightarrow & x = \frac{107}{330} & & \\ & V = \left\{ \frac{107}{330} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & 720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{420} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{420} & & \\ & V = \left\{ \frac{-109}{420} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{-36} & = & \color{red}{75x} +40 \\\Leftrightarrow & -135x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -135x-75x& = & 40+36 \\\Leftrightarrow & \color{red}{-210} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-210} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{9})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{8}{9}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+56} & = & \color{red}{189x} +90 \\\Leftrightarrow & -1260x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +90 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -1260x-189x& = & 90-56 \\\Leftrightarrow & \color{red}{-1449} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-1449} & & \\\Leftrightarrow & x = \frac{-34}{1449} & & \\ & V = \left\{ \frac{-34}{1449} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+98} & = & \color{red}{-168x} +27 \\\Leftrightarrow & -441x \color{red}{+98} \color{blue}{-98} \color{blue}{+168x} & = & \color{red}{-168x} +27 \color{blue}{+168x} \color{blue}{-98} \\\Leftrightarrow & -441x+168x& = & 27-98 \\\Leftrightarrow & \color{red}{-273} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-273} & & \\\Leftrightarrow & x = \frac{71}{273} & & \\ & V = \left\{ \frac{71}{273} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x+\frac{12}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+12} & = & \color{red}{35x} +4 \\\Leftrightarrow & -84x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -84x-35x& = & 4-12 \\\Leftrightarrow & \color{red}{-119} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-119} & & \\\Leftrightarrow & x = \frac{8}{119} & & \\ & V = \left\{ \frac{8}{119} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{196x} +49 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{-40} \\\Leftrightarrow & 280x-196x& = & 49-40 \\\Leftrightarrow & \color{red}{84} x& = & 9 \\\Leftrightarrow & x = \frac{9}{84} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{7})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -20x+\frac{12}{7}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+60} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -700x \color{red}{+60} \color{blue}{-60} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-60} \\\Leftrightarrow & -700x+105x& = & 56-60 \\\Leftrightarrow & \color{red}{-595} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-595} & & \\\Leftrightarrow & x = \frac{4}{595} & & \\ & V = \left\{ \frac{4}{595} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{9})& = & 2x+\frac{4}{9} \\\Leftrightarrow & 25x-\frac{25}{9}& = & 2x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x- \frac{25}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{-25} & = & \color{red}{18x} +4 \\\Leftrightarrow & 225x \color{red}{-25} \color{blue}{+25} \color{blue}{-18x} & = & \color{red}{18x} +4 \color{blue}{-18x} \color{blue}{+25} \\\Leftrightarrow & 225x-18x& = & 4+25 \\\Leftrightarrow & \color{red}{207} x& = & 29 \\\Leftrightarrow & x = \frac{29}{207} & & \\ & V = \left\{ \frac{29}{207} \right\} & \\\end{align}\)
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