Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+150} & = & \color{red}{-245x} +21 \\\Leftrightarrow & -1050x \color{red}{+150} \color{blue}{-150} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{-150} \\\Leftrightarrow & -1050x+245x& = & 21-150 \\\Leftrightarrow & \color{red}{-805} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{-805} & & \\\Leftrightarrow & x = \frac{129}{805} & & \\ & V = \left\{ \frac{129}{805} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1680x \color{red}{-192} & = & \color{red}{588x} +35 \\\Leftrightarrow & -1680x \color{red}{-192} \color{blue}{+192} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{+192} \\\Leftrightarrow & -1680x-588x& = & 35+192 \\\Leftrightarrow & \color{red}{-2268} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-2268} & & \\\Leftrightarrow & x = \frac{-227}{2268} & & \\ & V = \left\{ \frac{-227}{2268} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{154x} +33 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-24} \\\Leftrightarrow & -132x-154x& = & 33-24 \\\Leftrightarrow & \color{red}{-286} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-286} & & \\\Leftrightarrow & x = \frac{-9}{286} & & \\ & V = \left\{ \frac{-9}{286} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-168} & = & \color{red}{245x} +50 \\\Leftrightarrow & 1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & 1050x-245x& = & 50+168 \\\Leftrightarrow & \color{red}{805} x& = & 218 \\\Leftrightarrow & x = \frac{218}{805} & & \\ & V = \left\{ \frac{218}{805} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{12})& = & -4x+\frac{9}{10} \\\Leftrightarrow & -25x+\frac{25}{12}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{-240}{ \color{blue}{60} }x+ \frac{54}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{+125} & = & \color{red}{-240x} +54 \\\Leftrightarrow & -1500x \color{red}{+125} \color{blue}{-125} \color{blue}{+240x} & = & \color{red}{-240x} +54 \color{blue}{+240x} \color{blue}{-125} \\\Leftrightarrow & -1500x+240x& = & 54-125 \\\Leftrightarrow & \color{red}{-1260} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-1260} & & \\\Leftrightarrow & x = \frac{71}{1260} & & \\ & V = \left\{ \frac{71}{1260} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -14x-\frac{28}{9}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-882}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -882x \color{red}{-196} & = & \color{red}{315x} +81 \\\Leftrightarrow & -882x \color{red}{-196} \color{blue}{+196} \color{blue}{-315x} & = & \color{red}{315x} +81 \color{blue}{-315x} \color{blue}{+196} \\\Leftrightarrow & -882x-315x& = & 81+196 \\\Leftrightarrow & \color{red}{-1197} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-1197} & & \\\Leftrightarrow & x = \frac{-277}{1197} & & \\ & V = \left\{ \frac{-277}{1197} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -4x+\frac{5}{4} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{-80x} +25 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{-24} \\\Leftrightarrow & -300x+80x& = & 25-24 \\\Leftrightarrow & \color{red}{-220} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-220} & & \\\Leftrightarrow & x = \frac{-1}{220} & & \\ & V = \left\{ \frac{-1}{220} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{+100} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -700x \color{red}{+100} \color{blue}{-100} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{-100} \\\Leftrightarrow & -700x+490x& = & 63-100 \\\Leftrightarrow & \color{red}{-210} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-210} & & \\\Leftrightarrow & x = \frac{37}{210} & & \\ & V = \left\{ \frac{37}{210} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{9})& = & 6x+\frac{3}{10} \\\Leftrightarrow & -35x+\frac{28}{9}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-3150}{ \color{blue}{90} }x+ \frac{280}{ \color{blue}{90} })& = & (\frac{540}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -3150x \color{red}{+280} & = & \color{red}{540x} +27 \\\Leftrightarrow & -3150x \color{red}{+280} \color{blue}{-280} \color{blue}{-540x} & = & \color{red}{540x} +27 \color{blue}{-540x} \color{blue}{-280} \\\Leftrightarrow & -3150x-540x& = & 27-280 \\\Leftrightarrow & \color{red}{-3690} x& = & -253 \\\Leftrightarrow & x = \frac{-253}{-3690} & & \\\Leftrightarrow & x = \frac{253}{3690} & & \\ & V = \left\{ \frac{253}{3690} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -4x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+108} & = & \color{red}{-180x} +10 \\\Leftrightarrow & 675x \color{red}{+108} \color{blue}{-108} \color{blue}{+180x} & = & \color{red}{-180x} +10 \color{blue}{+180x} \color{blue}{-108} \\\Leftrightarrow & 675x+180x& = & 10-108 \\\Leftrightarrow & \color{red}{855} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{855} & & \\ & V = \left\{ \frac{-98}{855} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 25x-\frac{25}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{-75} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 825x \color{red}{-75} \color{blue}{+75} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+75} \\\Leftrightarrow & 825x+297x& = & 44+75 \\\Leftrightarrow & \color{red}{1122} x& = & 119 \\\Leftrightarrow & x = \frac{119}{1122} & & \\\Leftrightarrow & x = \frac{7}{66} & & \\ & V = \left\{ \frac{7}{66} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{20}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-220} & = & \color{red}{693x} +54 \\\Leftrightarrow & -1584x \color{red}{-220} \color{blue}{+220} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+220} \\\Leftrightarrow & -1584x-693x& = & 54+220 \\\Leftrightarrow & \color{red}{-2277} x& = & 274 \\\Leftrightarrow & x = \frac{274}{-2277} & & \\\Leftrightarrow & x = \frac{-274}{2277} & & \\ & V = \left\{ \frac{-274}{2277} \right\} & \\\end{align}\)
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