Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{840}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{196x} +63 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{-120} \\\Leftrightarrow & 840x-196x& = & 63-120 \\\Leftrightarrow & \color{red}{644} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{644} & & \\ & V = \left\{ \frac{-57}{644} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+140} & = & \color{red}{-567x} +81 \\\Leftrightarrow & -1260x \color{red}{+140} \color{blue}{-140} \color{blue}{+567x} & = & \color{red}{-567x} +81 \color{blue}{+567x} \color{blue}{-140} \\\Leftrightarrow & -1260x+567x& = & 81-140 \\\Leftrightarrow & \color{red}{-693} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-693} & & \\\Leftrightarrow & x = \frac{59}{693} & & \\ & V = \left\{ \frac{59}{693} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-6} & = & \color{red}{63x} +10 \\\Leftrightarrow & -56x \color{red}{-6} \color{blue}{+6} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+6} \\\Leftrightarrow & -56x-63x& = & 10+6 \\\Leftrightarrow & \color{red}{-119} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-119} & & \\\Leftrightarrow & x = \frac{-16}{119} & & \\ & V = \left\{ \frac{-16}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{165x} +44 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-72} \\\Leftrightarrow & -792x-165x& = & 44-72 \\\Leftrightarrow & \color{red}{-957} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-957} & & \\\Leftrightarrow & x = \frac{28}{957} & & \\ & V = \left\{ \frac{28}{957} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{9})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{-81x} +10 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & -36x+81x& = & 10-8 \\\Leftrightarrow & \color{red}{45} x& = & 2 \\\Leftrightarrow & x = \frac{2}{45} & & \\ & V = \left\{ \frac{2}{45} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{35x} +8 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -63x-35x& = & 8+6 \\\Leftrightarrow & \color{red}{-98} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-98} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{11})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 14x+\frac{28}{11}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x+ \frac{252}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{+252} & = & \color{red}{891x} +22 \\\Leftrightarrow & 1386x \color{red}{+252} \color{blue}{-252} \color{blue}{-891x} & = & \color{red}{891x} +22 \color{blue}{-891x} \color{blue}{-252} \\\Leftrightarrow & 1386x-891x& = & 22-252 \\\Leftrightarrow & \color{red}{495} x& = & -230 \\\Leftrightarrow & x = \frac{-230}{495} & & \\\Leftrightarrow & x = \frac{-46}{99} & & \\ & V = \left\{ \frac{-46}{99} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{11})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 18x+\frac{12}{11}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+60} & = & \color{red}{275x} +99 \\\Leftrightarrow & 990x \color{red}{+60} \color{blue}{-60} \color{blue}{-275x} & = & \color{red}{275x} +99 \color{blue}{-275x} \color{blue}{-60} \\\Leftrightarrow & 990x-275x& = & 99-60 \\\Leftrightarrow & \color{red}{715} x& = & 39 \\\Leftrightarrow & x = \frac{39}{715} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-175x} +25 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +25 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 420x+175x& = & 25-84 \\\Leftrightarrow & \color{red}{595} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{595} & & \\ & V = \left\{ \frac{-59}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -90x+35x& = & 8+12 \\\Leftrightarrow & \color{red}{-55} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-55} & & \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{7})& = & -9x+\frac{5}{8} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-160} & = & \color{red}{-504x} +35 \\\Leftrightarrow & -1120x \color{red}{-160} \color{blue}{+160} \color{blue}{+504x} & = & \color{red}{-504x} +35 \color{blue}{+504x} \color{blue}{+160} \\\Leftrightarrow & -1120x+504x& = & 35+160 \\\Leftrightarrow & \color{red}{-616} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-616} & & \\\Leftrightarrow & x = \frac{-195}{616} & & \\ & V = \left\{ \frac{-195}{616} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{7})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 16x+\frac{12}{7}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{448}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 448x \color{red}{+48} & = & \color{red}{84x} +63 \\\Leftrightarrow & 448x \color{red}{+48} \color{blue}{-48} \color{blue}{-84x} & = & \color{red}{84x} +63 \color{blue}{-84x} \color{blue}{-48} \\\Leftrightarrow & 448x-84x& = & 63-48 \\\Leftrightarrow & \color{red}{364} x& = & 15 \\\Leftrightarrow & x = \frac{15}{364} & & \\ & V = \left\{ \frac{15}{364} \right\} & \\\end{align}\)
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