Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{2})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{15}{2}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+75} & = & \color{red}{70x} +14 \\\Leftrightarrow & 150x \color{red}{+75} \color{blue}{-75} \color{blue}{-70x} & = & \color{red}{70x} +14 \color{blue}{-70x} \color{blue}{-75} \\\Leftrightarrow & 150x-70x& = & 14-75 \\\Leftrightarrow & \color{red}{80} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{80} & & \\ & V = \left\{ \frac{-61}{80} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{3})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -35x+\frac{35}{3}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{+35} & = & \color{red}{9x} +5 \\\Leftrightarrow & -105x \color{red}{+35} \color{blue}{-35} \color{blue}{-9x} & = & \color{red}{9x} +5 \color{blue}{-9x} \color{blue}{-35} \\\Leftrightarrow & -105x-9x& = & 5-35 \\\Leftrightarrow & \color{red}{-114} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{-114} & & \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{11})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{4}{11}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{880}{ \color{blue}{110} }x- \frac{40}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 880x \color{red}{-40} & = & \color{red}{-330x} +33 \\\Leftrightarrow & 880x \color{red}{-40} \color{blue}{+40} \color{blue}{+330x} & = & \color{red}{-330x} +33 \color{blue}{+330x} \color{blue}{+40} \\\Leftrightarrow & 880x+330x& = & 33+40 \\\Leftrightarrow & \color{red}{1210} x& = & 73 \\\Leftrightarrow & x = \frac{73}{1210} & & \\ & V = \left\{ \frac{73}{1210} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -4x+\frac{7}{4} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -4x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-792}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -792x \color{red}{-72} & = & \color{red}{-176x} +77 \\\Leftrightarrow & -792x \color{red}{-72} \color{blue}{+72} \color{blue}{+176x} & = & \color{red}{-176x} +77 \color{blue}{+176x} \color{blue}{+72} \\\Leftrightarrow & -792x+176x& = & 77+72 \\\Leftrightarrow & \color{red}{-616} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-616} & & \\\Leftrightarrow & x = \frac{-149}{616} & & \\ & V = \left\{ \frac{-149}{616} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -4x+\frac{5}{8} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -4x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{-48} & = & \color{red}{-224x} +35 \\\Leftrightarrow & 840x \color{red}{-48} \color{blue}{+48} \color{blue}{+224x} & = & \color{red}{-224x} +35 \color{blue}{+224x} \color{blue}{+48} \\\Leftrightarrow & 840x+224x& = & 35+48 \\\Leftrightarrow & \color{red}{1064} x& = & 83 \\\Leftrightarrow & x = \frac{83}{1064} & & \\ & V = \left\{ \frac{83}{1064} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -2x+\frac{7}{5} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+105} & = & \color{red}{-80x} +56 \\\Leftrightarrow & -1120x \color{red}{+105} \color{blue}{-105} \color{blue}{+80x} & = & \color{red}{-80x} +56 \color{blue}{+80x} \color{blue}{-105} \\\Leftrightarrow & -1120x+80x& = & 56-105 \\\Leftrightarrow & \color{red}{-1040} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-1040} & & \\\Leftrightarrow & x = \frac{49}{1040} & & \\ & V = \left\{ \frac{49}{1040} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{4})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{15}{4}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-135} & = & \color{red}{-108x} +16 \\\Leftrightarrow & 720x \color{red}{-135} \color{blue}{+135} \color{blue}{+108x} & = & \color{red}{-108x} +16 \color{blue}{+108x} \color{blue}{+135} \\\Leftrightarrow & 720x+108x& = & 16+135 \\\Leftrightarrow & \color{red}{828} x& = & 151 \\\Leftrightarrow & x = \frac{151}{828} & & \\ & V = \left\{ \frac{151}{828} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{15}{4}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{140x} +18 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{-140x} & = & \color{red}{140x} +18 \color{blue}{-140x} \color{blue}{-75} \\\Leftrightarrow & 400x-140x& = & 18-75 \\\Leftrightarrow & \color{red}{260} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{260} & & \\ & V = \left\{ \frac{-57}{260} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+8} & = & \color{red}{-9x} +8 \\\Leftrightarrow & 48x \color{red}{+8} \color{blue}{-8} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{-8} \\\Leftrightarrow & 48x+9x& = & 8-8 \\\Leftrightarrow & \color{red}{57} x& = & 0 \\\Leftrightarrow & x = \frac{0}{57} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{576}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 576x \color{red}{+64} & = & \color{red}{-216x} +63 \\\Leftrightarrow & 576x \color{red}{+64} \color{blue}{-64} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{-64} \\\Leftrightarrow & 576x+216x& = & 63-64 \\\Leftrightarrow & \color{red}{792} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{792} & & \\ & V = \left\{ \frac{-1}{792} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & -2x+\frac{2}{7} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -2x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x- \frac{196}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{-196} & = & \color{red}{-70x} +10 \\\Leftrightarrow & 735x \color{red}{-196} \color{blue}{+196} \color{blue}{+70x} & = & \color{red}{-70x} +10 \color{blue}{+70x} \color{blue}{+196} \\\Leftrightarrow & 735x+70x& = & 10+196 \\\Leftrightarrow & \color{red}{805} x& = & 206 \\\Leftrightarrow & x = \frac{206}{805} & & \\ & V = \left\{ \frac{206}{805} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-220} & = & \color{red}{165x} +24 \\\Leftrightarrow & -396x \color{red}{-220} \color{blue}{+220} \color{blue}{-165x} & = & \color{red}{165x} +24 \color{blue}{-165x} \color{blue}{+220} \\\Leftrightarrow & -396x-165x& = & 24+220 \\\Leftrightarrow & \color{red}{-561} x& = & 244 \\\Leftrightarrow & x = \frac{244}{-561} & & \\\Leftrightarrow & x = \frac{-244}{561} & & \\ & V = \left\{ \frac{-244}{561} \right\} & \\\end{align}\)
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