Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{8}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{168x} +24 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{-168x} & = & \color{red}{168x} +24 \color{blue}{-168x} \color{blue}{+98} \\\Leftrightarrow & -441x-168x& = & 24+98 \\\Leftrightarrow & \color{red}{-609} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-609} & & \\\Leftrightarrow & x = \frac{-122}{609} & & \\ & V = \left\{ \frac{-122}{609} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{25}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{-125} & = & \color{red}{385x} +44 \\\Leftrightarrow & 1100x \color{red}{-125} \color{blue}{+125} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+125} \\\Leftrightarrow & 1100x-385x& = & 44+125 \\\Leftrightarrow & \color{red}{715} x& = & 169 \\\Leftrightarrow & x = \frac{169}{715} & & \\\Leftrightarrow & x = \frac{13}{55} & & \\ & V = \left\{ \frac{13}{55} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{11})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{16}{11}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+80} & = & \color{red}{-495x} +66 \\\Leftrightarrow & -440x \color{red}{+80} \color{blue}{-80} \color{blue}{+495x} & = & \color{red}{-495x} +66 \color{blue}{+495x} \color{blue}{-80} \\\Leftrightarrow & -440x+495x& = & 66-80 \\\Leftrightarrow & \color{red}{55} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{55} & & \\ & V = \left\{ \frac{-14}{55} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-270} & = & \color{red}{-315x} +70 \\\Leftrightarrow & 756x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & 756x+315x& = & 70+270 \\\Leftrightarrow & \color{red}{1071} x& = & 340 \\\Leftrightarrow & x = \frac{340}{1071} & & \\\Leftrightarrow & x = \frac{20}{63} & & \\ & V = \left\{ \frac{20}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{-120} & = & \color{red}{196x} +35 \\\Leftrightarrow & 672x \color{red}{-120} \color{blue}{+120} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{+120} \\\Leftrightarrow & 672x-196x& = & 35+120 \\\Leftrightarrow & \color{red}{476} x& = & 155 \\\Leftrightarrow & x = \frac{155}{476} & & \\ & V = \left\{ \frac{155}{476} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+4} \\\Leftrightarrow & -30x+21x& = & 10+4 \\\Leftrightarrow & \color{red}{-9} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-9} & & \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-132} & = & \color{red}{275x} +40 \\\Leftrightarrow & -1320x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -1320x-275x& = & 40+132 \\\Leftrightarrow & \color{red}{-1595} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1595} & & \\\Leftrightarrow & x = \frac{-172}{1595} & & \\ & V = \left\{ \frac{-172}{1595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +10 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 10-6 \\\Leftrightarrow & \color{red}{-119} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-119} & & \\\Leftrightarrow & x = \frac{-4}{119} & & \\ & V = \left\{ \frac{-4}{119} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{4})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{-45} & = & \color{red}{-84x} +40 \\\Leftrightarrow & -72x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +40 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & -72x+84x& = & 40+45 \\\Leftrightarrow & \color{red}{12} x& = & 85 \\\Leftrightarrow & x = \frac{85}{12} & & \\ & V = \left\{ \frac{85}{12} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{+80} & = & \color{red}{-210x} +9 \\\Leftrightarrow & -300x \color{red}{+80} \color{blue}{-80} \color{blue}{+210x} & = & \color{red}{-210x} +9 \color{blue}{+210x} \color{blue}{-80} \\\Leftrightarrow & -300x+210x& = & 9-80 \\\Leftrightarrow & \color{red}{-90} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-90} & & \\\Leftrightarrow & x = \frac{71}{90} & & \\ & V = \left\{ \frac{71}{90} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{-24} & = & \color{red}{-50x} +25 \\\Leftrightarrow & -240x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -240x+50x& = & 25+24 \\\Leftrightarrow & \color{red}{-190} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-190} & & \\\Leftrightarrow & x = \frac{-49}{190} & & \\ & V = \left\{ \frac{-49}{190} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{4})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{35}{4}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{105}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-105} & = & \color{red}{-108x} +40 \\\Leftrightarrow & -420x \color{red}{-105} \color{blue}{+105} \color{blue}{+108x} & = & \color{red}{-108x} +40 \color{blue}{+108x} \color{blue}{+105} \\\Leftrightarrow & -420x+108x& = & 40+105 \\\Leftrightarrow & \color{red}{-312} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-312} & & \\\Leftrightarrow & x = \frac{-145}{312} & & \\ & V = \left\{ \frac{-145}{312} \right\} & \\\end{align}\)
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