Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 180x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 180x+63x& = & 6+8 \\\Leftrightarrow & \color{red}{243} x& = & 14 \\\Leftrightarrow & x = \frac{14}{243} & & \\ & V = \left\{ \frac{14}{243} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{9})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{25}{9}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+50} & = & \color{red}{36x} +15 \\\Leftrightarrow & 270x \color{red}{+50} \color{blue}{-50} \color{blue}{-36x} & = & \color{red}{36x} +15 \color{blue}{-36x} \color{blue}{-50} \\\Leftrightarrow & 270x-36x& = & 15-50 \\\Leftrightarrow & \color{red}{234} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{234} & & \\ & V = \left\{ \frac{-35}{234} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{9})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -15x-\frac{25}{9}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-175} & = & \color{red}{-252x} +72 \\\Leftrightarrow & -945x \color{red}{-175} \color{blue}{+175} \color{blue}{+252x} & = & \color{red}{-252x} +72 \color{blue}{+252x} \color{blue}{+175} \\\Leftrightarrow & -945x+252x& = & 72+175 \\\Leftrightarrow & \color{red}{-693} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-693} & & \\\Leftrightarrow & x = \frac{-247}{693} & & \\ & V = \left\{ \frac{-247}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+10} & = & \color{red}{49x} +8 \\\Leftrightarrow & -70x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & -70x-49x& = & 8-10 \\\Leftrightarrow & \color{red}{-119} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-119} & & \\\Leftrightarrow & x = \frac{2}{119} & & \\ & V = \left\{ \frac{2}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -14x-\frac{14}{9}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x- \frac{28}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{54x} +45 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +45 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & -252x-54x& = & 45+28 \\\Leftrightarrow & \color{red}{-306} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-306} & & \\\Leftrightarrow & x = \frac{-73}{306} & & \\ & V = \left\{ \frac{-73}{306} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-220} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 924x \color{red}{-220} \color{blue}{+220} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+220} \\\Leftrightarrow & 924x+385x& = & 70+220 \\\Leftrightarrow & \color{red}{1309} x& = & 290 \\\Leftrightarrow & x = \frac{290}{1309} & & \\ & V = \left\{ \frac{290}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{9})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{25}{9}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+175} & = & \color{red}{-252x} +90 \\\Leftrightarrow & 945x \color{red}{+175} \color{blue}{-175} \color{blue}{+252x} & = & \color{red}{-252x} +90 \color{blue}{+252x} \color{blue}{-175} \\\Leftrightarrow & 945x+252x& = & 90-175 \\\Leftrightarrow & \color{red}{1197} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{1197} & & \\ & V = \left\{ \frac{-85}{1197} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 14x-\frac{14}{11}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{98}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-98} & = & \color{red}{231x} +66 \\\Leftrightarrow & 1078x \color{red}{-98} \color{blue}{+98} \color{blue}{-231x} & = & \color{red}{231x} +66 \color{blue}{-231x} \color{blue}{+98} \\\Leftrightarrow & 1078x-231x& = & 66+98 \\\Leftrightarrow & \color{red}{847} x& = & 164 \\\Leftrightarrow & x = \frac{164}{847} & & \\ & V = \left\{ \frac{164}{847} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{9})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{-220} & = & \color{red}{891x} +81 \\\Leftrightarrow & -2475x \color{red}{-220} \color{blue}{+220} \color{blue}{-891x} & = & \color{red}{891x} +81 \color{blue}{-891x} \color{blue}{+220} \\\Leftrightarrow & -2475x-891x& = & 81+220 \\\Leftrightarrow & \color{red}{-3366} x& = & 301 \\\Leftrightarrow & x = \frac{301}{-3366} & & \\\Leftrightarrow & x = \frac{-301}{3366} & & \\ & V = \left\{ \frac{-301}{3366} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{275x} +33 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-275x} & = & \color{red}{275x} +33 \color{blue}{-275x} \color{blue}{-120} \\\Leftrightarrow & 1320x-275x& = & 33-120 \\\Leftrightarrow & \color{red}{1045} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{1045} & & \\ & V = \left\{ \frac{-87}{1045} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{9})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{10}{9}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{+20} & = & \color{red}{144x} +63 \\\Leftrightarrow & -270x \color{red}{+20} \color{blue}{-20} \color{blue}{-144x} & = & \color{red}{144x} +63 \color{blue}{-144x} \color{blue}{-20} \\\Leftrightarrow & -270x-144x& = & 63-20 \\\Leftrightarrow & \color{red}{-414} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-414} & & \\\Leftrightarrow & x = \frac{-43}{414} & & \\ & V = \left\{ \frac{-43}{414} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-18} \\\Leftrightarrow & 120x-50x& = & 45-18 \\\Leftrightarrow & \color{red}{70} x& = & 27 \\\Leftrightarrow & x = \frac{27}{70} & & \\ & V = \left\{ \frac{27}{70} \right\} & \\\end{align}\)