Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{4})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 9x-\frac{9}{4}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x- \frac{63}{ \color{blue}{28} })& = & (\frac{112}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-63} & = & \color{red}{112x} +8 \\\Leftrightarrow & 252x \color{red}{-63} \color{blue}{+63} \color{blue}{-112x} & = & \color{red}{112x} +8 \color{blue}{-112x} \color{blue}{+63} \\\Leftrightarrow & 252x-112x& = & 8+63 \\\Leftrightarrow & \color{red}{140} x& = & 71 \\\Leftrightarrow & x = \frac{71}{140} & & \\ & V = \left\{ \frac{71}{140} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{9})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x+\frac{4}{9}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{+8} & = & \color{red}{-90x} +15 \\\Leftrightarrow & 108x \color{red}{+8} \color{blue}{-8} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{-8} \\\Leftrightarrow & 108x+90x& = & 15-8 \\\Leftrightarrow & \color{red}{198} x& = & 7 \\\Leftrightarrow & x = \frac{7}{198} & & \\ & V = \left\{ \frac{7}{198} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{11})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{8}{11}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+40} \\\Leftrightarrow & -440x+165x& = & 44+40 \\\Leftrightarrow & \color{red}{-275} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-275} & & \\\Leftrightarrow & x = \frac{-84}{275} & & \\ & V = \left\{ \frac{-84}{275} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{-270} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & 1512x+441x& = & 70+270 \\\Leftrightarrow & \color{red}{1953} x& = & 340 \\\Leftrightarrow & x = \frac{340}{1953} & & \\ & V = \left\{ \frac{340}{1953} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{12})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 20x+\frac{25}{12}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1680}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1680x \color{red}{+175} & = & \color{red}{588x} +48 \\\Leftrightarrow & 1680x \color{red}{+175} \color{blue}{-175} \color{blue}{-588x} & = & \color{red}{588x} +48 \color{blue}{-588x} \color{blue}{-175} \\\Leftrightarrow & 1680x-588x& = & 48-175 \\\Leftrightarrow & \color{red}{1092} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1092} & & \\ & V = \left\{ \frac{-127}{1092} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 2x+\frac{9}{11} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 2x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-66} & = & \color{red}{154x} +63 \\\Leftrightarrow & 693x \color{red}{-66} \color{blue}{+66} \color{blue}{-154x} & = & \color{red}{154x} +63 \color{blue}{-154x} \color{blue}{+66} \\\Leftrightarrow & 693x-154x& = & 63+66 \\\Leftrightarrow & \color{red}{539} x& = & 129 \\\Leftrightarrow & x = \frac{129}{539} & & \\ & V = \left\{ \frac{129}{539} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -4x-\frac{6}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-42} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -308x \color{red}{-42} \color{blue}{+42} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+42} \\\Leftrightarrow & -308x+385x& = & 44+42 \\\Leftrightarrow & \color{red}{77} x& = & 86 \\\Leftrightarrow & x = \frac{86}{77} & & \\ & V = \left\{ \frac{86}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{11})& = & 4x+\frac{2}{7} \\\Leftrightarrow & -15x+\frac{10}{11}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+70} & = & \color{red}{308x} +22 \\\Leftrightarrow & -1155x \color{red}{+70} \color{blue}{-70} \color{blue}{-308x} & = & \color{red}{308x} +22 \color{blue}{-308x} \color{blue}{-70} \\\Leftrightarrow & -1155x-308x& = & 22-70 \\\Leftrightarrow & \color{red}{-1463} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-1463} & & \\\Leftrightarrow & x = \frac{48}{1463} & & \\ & V = \left\{ \frac{48}{1463} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x-\frac{8}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-88} & = & \color{red}{231x} +28 \\\Leftrightarrow & 616x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & 616x-231x& = & 28+88 \\\Leftrightarrow & \color{red}{385} x& = & 116 \\\Leftrightarrow & x = \frac{116}{385} & & \\ & V = \left\{ \frac{116}{385} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -240x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{-345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-345} & & \\\Leftrightarrow & x = \frac{26}{345} & & \\ & V = \left\{ \frac{26}{345} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-60} & = & \color{red}{308x} +55 \\\Leftrightarrow & -440x \color{red}{-60} \color{blue}{+60} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{+60} \\\Leftrightarrow & -440x-308x& = & 55+60 \\\Leftrightarrow & \color{red}{-748} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-748} & & \\\Leftrightarrow & x = \frac{-115}{748} & & \\ & V = \left\{ \frac{-115}{748} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & -770x+539x& = & 42-110 \\\Leftrightarrow & \color{red}{-231} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-231} & & \\\Leftrightarrow & x = \frac{68}{231} & & \\ & V = \left\{ \frac{68}{231} \right\} & \\\end{align}\)
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