Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{30}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-150} & = & \color{red}{275x} +66 \\\Leftrightarrow & 990x \color{red}{-150} \color{blue}{+150} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+150} \\\Leftrightarrow & 990x-275x& = & 66+150 \\\Leftrightarrow & \color{red}{715} x& = & 216 \\\Leftrightarrow & x = \frac{216}{715} & & \\ & V = \left\{ \frac{216}{715} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{8})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -14x+\frac{35}{8}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{105}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+105} & = & \color{red}{72x} +32 \\\Leftrightarrow & -336x \color{red}{+105} \color{blue}{-105} \color{blue}{-72x} & = & \color{red}{72x} +32 \color{blue}{-72x} \color{blue}{-105} \\\Leftrightarrow & -336x-72x& = & 32-105 \\\Leftrightarrow & \color{red}{-408} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-408} & & \\\Leftrightarrow & x = \frac{73}{408} & & \\ & V = \left\{ \frac{73}{408} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1440}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1440x \color{red}{-160} & = & \color{red}{216x} +63 \\\Leftrightarrow & -1440x \color{red}{-160} \color{blue}{+160} \color{blue}{-216x} & = & \color{red}{216x} +63 \color{blue}{-216x} \color{blue}{+160} \\\Leftrightarrow & -1440x-216x& = & 63+160 \\\Leftrightarrow & \color{red}{-1656} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-1656} & & \\\Leftrightarrow & x = \frac{-223}{1656} & & \\ & V = \left\{ \frac{-223}{1656} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-36} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -90x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -90x+105x& = & 40+36 \\\Leftrightarrow & \color{red}{15} x& = & 76 \\\Leftrightarrow & x = \frac{76}{15} & & \\ & V = \left\{ \frac{76}{15} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{8})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -9x+\frac{15}{8}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-504}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -504x \color{red}{+105} & = & \color{red}{-392x} +48 \\\Leftrightarrow & -504x \color{red}{+105} \color{blue}{-105} \color{blue}{+392x} & = & \color{red}{-392x} +48 \color{blue}{+392x} \color{blue}{-105} \\\Leftrightarrow & -504x+392x& = & 48-105 \\\Leftrightarrow & \color{red}{-112} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-112} & & \\\Leftrightarrow & x = \frac{57}{112} & & \\ & V = \left\{ \frac{57}{112} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{75x} +40 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+18} \\\Leftrightarrow & 90x-75x& = & 40+18 \\\Leftrightarrow & \color{red}{15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{15} & & \\ & V = \left\{ \frac{58}{15} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -8x-\frac{6}{11}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-42} & = & \color{red}{-693x} +33 \\\Leftrightarrow & -616x \color{red}{-42} \color{blue}{+42} \color{blue}{+693x} & = & \color{red}{-693x} +33 \color{blue}{+693x} \color{blue}{+42} \\\Leftrightarrow & -616x+693x& = & 33+42 \\\Leftrightarrow & \color{red}{77} x& = & 75 \\\Leftrightarrow & x = \frac{75}{77} & & \\ & V = \left\{ \frac{75}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-80} & = & \color{red}{-196x} +35 \\\Leftrightarrow & 420x \color{red}{-80} \color{blue}{+80} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{+80} \\\Leftrightarrow & 420x+196x& = & 35+80 \\\Leftrightarrow & \color{red}{616} x& = & 115 \\\Leftrightarrow & x = \frac{115}{616} & & \\ & V = \left\{ \frac{115}{616} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-216} & = & \color{red}{-225x} +20 \\\Leftrightarrow & 540x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +20 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 540x+225x& = & 20+216 \\\Leftrightarrow & \color{red}{765} x& = & 236 \\\Leftrightarrow & x = \frac{236}{765} & & \\ & V = \left\{ \frac{236}{765} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 18x-\frac{12}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-60} & = & \color{red}{-275x} +88 \\\Leftrightarrow & 990x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & 990x+275x& = & 88+60 \\\Leftrightarrow & \color{red}{1265} x& = & 148 \\\Leftrightarrow & x = \frac{148}{1265} & & \\ & V = \left\{ \frac{148}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{20}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{+45} & = & \color{red}{-60x} +20 \\\Leftrightarrow & 72x \color{red}{+45} \color{blue}{-45} \color{blue}{+60x} & = & \color{red}{-60x} +20 \color{blue}{+60x} \color{blue}{-45} \\\Leftrightarrow & 72x+60x& = & 20-45 \\\Leftrightarrow & \color{red}{132} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{132} & & \\ & V = \left\{ \frac{-25}{132} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-18} \\\Leftrightarrow & 120x+100x& = & 45-18 \\\Leftrightarrow & \color{red}{220} x& = & 27 \\\Leftrightarrow & x = \frac{27}{220} & & \\ & V = \left\{ \frac{27}{220} \right\} & \\\end{align}\)
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