Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{+18} & = & \color{red}{-35x} +7 \\\Leftrightarrow & -150x \color{red}{+18} \color{blue}{-18} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{-18} \\\Leftrightarrow & -150x+35x& = & 7-18 \\\Leftrightarrow & \color{red}{-115} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-115} & & \\\Leftrightarrow & x = \frac{11}{115} & & \\ & V = \left\{ \frac{11}{115} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+220} & = & \color{red}{231x} +27 \\\Leftrightarrow & -528x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +27 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & -528x-231x& = & 27-220 \\\Leftrightarrow & \color{red}{-759} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{-759} & & \\\Leftrightarrow & x = \frac{193}{759} & & \\ & V = \left\{ \frac{193}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{245x} +49 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & -210x-245x& = & 49+30 \\\Leftrightarrow & \color{red}{-455} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-455} & & \\\Leftrightarrow & x = \frac{-79}{455} & & \\ & V = \left\{ \frac{-79}{455} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-66} & = & \color{red}{385x} +56 \\\Leftrightarrow & -924x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -924x-385x& = & 56+66 \\\Leftrightarrow & \color{red}{-1309} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-1309} & & \\\Leftrightarrow & x = \frac{-122}{1309} & & \\ & V = \left\{ \frac{-122}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{25}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+50} & = & \color{red}{126x} +81 \\\Leftrightarrow & -360x \color{red}{+50} \color{blue}{-50} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{-50} \\\Leftrightarrow & -360x-126x& = & 81-50 \\\Leftrightarrow & \color{red}{-486} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-486} & & \\\Leftrightarrow & x = \frac{-31}{486} & & \\ & V = \left\{ \frac{-31}{486} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{392x} +35 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{-392x} & = & \color{red}{392x} +35 \color{blue}{-392x} \color{blue}{+80} \\\Leftrightarrow & 560x-392x& = & 35+80 \\\Leftrightarrow & \color{red}{168} x& = & 115 \\\Leftrightarrow & x = \frac{115}{168} & & \\ & V = \left\{ \frac{115}{168} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{3})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{28}{3}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-28} & = & \color{red}{-6x} +4 \\\Leftrightarrow & 63x \color{red}{-28} \color{blue}{+28} \color{blue}{+6x} & = & \color{red}{-6x} +4 \color{blue}{+6x} \color{blue}{+28} \\\Leftrightarrow & 63x+6x& = & 4+28 \\\Leftrightarrow & \color{red}{69} x& = & 32 \\\Leftrightarrow & x = \frac{32}{69} & & \\ & V = \left\{ \frac{32}{69} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-126} & = & \color{red}{-308x} +88 \\\Leftrightarrow & -1386x \color{red}{-126} \color{blue}{+126} \color{blue}{+308x} & = & \color{red}{-308x} +88 \color{blue}{+308x} \color{blue}{+126} \\\Leftrightarrow & -1386x+308x& = & 88+126 \\\Leftrightarrow & \color{red}{-1078} x& = & 214 \\\Leftrightarrow & x = \frac{214}{-1078} & & \\\Leftrightarrow & x = \frac{-107}{539} & & \\ & V = \left\{ \frac{-107}{539} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-40} & = & \color{red}{135x} +24 \\\Leftrightarrow & 150x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & 150x-135x& = & 24+40 \\\Leftrightarrow & \color{red}{15} x& = & 64 \\\Leftrightarrow & x = \frac{64}{15} & & \\ & V = \left\{ \frac{64}{15} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{-297x} +12 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+297x} & = & \color{red}{-297x} +12 \color{blue}{+297x} \color{blue}{+154} \\\Leftrightarrow & -1155x+297x& = & 12+154 \\\Leftrightarrow & \color{red}{-858} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-858} & & \\\Leftrightarrow & x = \frac{-83}{429} & & \\ & V = \left\{ \frac{-83}{429} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+270} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -2970x \color{red}{+270} \color{blue}{-270} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-270} \\\Leftrightarrow & -2970x+693x& = & 110-270 \\\Leftrightarrow & \color{red}{-2277} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{-2277} & & \\\Leftrightarrow & x = \frac{160}{2277} & & \\ & V = \left\{ \frac{160}{2277} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-105} & = & \color{red}{196x} +40 \\\Leftrightarrow & -168x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +40 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & -168x-196x& = & 40+105 \\\Leftrightarrow & \color{red}{-364} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-364} & & \\\Leftrightarrow & x = \frac{-145}{364} & & \\ & V = \left\{ \frac{-145}{364} \right\} & \\\end{align}\)
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