Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{9}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +63 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +63 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 63-150 \\\Leftrightarrow & \color{red}{-595} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-595} & & \\\Leftrightarrow & x = \frac{87}{595} & & \\ & V = \left\{ \frac{87}{595} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{9})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-16} & = & \color{red}{-162x} +27 \\\Leftrightarrow & -144x \color{red}{-16} \color{blue}{+16} \color{blue}{+162x} & = & \color{red}{-162x} +27 \color{blue}{+162x} \color{blue}{+16} \\\Leftrightarrow & -144x+162x& = & 27+16 \\\Leftrightarrow & \color{red}{18} x& = & 43 \\\Leftrightarrow & x = \frac{43}{18} & & \\ & V = \left\{ \frac{43}{18} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{385x} +30 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1650x-385x& = & 30+264 \\\Leftrightarrow & \color{red}{1265} x& = & 294 \\\Leftrightarrow & x = \frac{294}{1265} & & \\ & V = \left\{ \frac{294}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+220} & = & \color{red}{-385x} +70 \\\Leftrightarrow & -924x \color{red}{+220} \color{blue}{-220} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{-220} \\\Leftrightarrow & -924x+385x& = & 70-220 \\\Leftrightarrow & \color{red}{-539} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{-539} & & \\\Leftrightarrow & x = \frac{150}{539} & & \\ & V = \left\{ \frac{150}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{4}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-50}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -50x \color{red}{-4} & = & \color{red}{35x} +6 \\\Leftrightarrow & -50x \color{red}{-4} \color{blue}{+4} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+4} \\\Leftrightarrow & -50x-35x& = & 6+4 \\\Leftrightarrow & \color{red}{-85} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-85} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{2})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 9x+\frac{9}{2}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{18}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 18x \color{red}{+9} & = & \color{red}{-14x} +3 \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{+14x} & = & \color{red}{-14x} +3 \color{blue}{+14x} \color{blue}{-9} \\\Leftrightarrow & 18x+14x& = & 3-9 \\\Leftrightarrow & \color{red}{32} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{32} & & \\\Leftrightarrow & x = \frac{-3}{16} & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & -2x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-8}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{-15} & = & \color{red}{-8x} +14 \\\Leftrightarrow & 60x \color{red}{-15} \color{blue}{+15} \color{blue}{+8x} & = & \color{red}{-8x} +14 \color{blue}{+8x} \color{blue}{+15} \\\Leftrightarrow & 60x+8x& = & 14+15 \\\Leftrightarrow & \color{red}{68} x& = & 29 \\\Leftrightarrow & x = \frac{29}{68} & & \\ & V = \left\{ \frac{29}{68} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{8}{9}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+8} & = & \color{red}{27x} +4 \\\Leftrightarrow & -180x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & -180x-27x& = & 4-8 \\\Leftrightarrow & \color{red}{-207} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-207} & & \\\Leftrightarrow & x = \frac{4}{207} & & \\ & V = \left\{ \frac{4}{207} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{7})& = & -2x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{15}{7}& = & -2x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-75} & = & \color{red}{-70x} +56 \\\Leftrightarrow & 525x \color{red}{-75} \color{blue}{+75} \color{blue}{+70x} & = & \color{red}{-70x} +56 \color{blue}{+70x} \color{blue}{+75} \\\Leftrightarrow & 525x+70x& = & 56+75 \\\Leftrightarrow & \color{red}{595} x& = & 131 \\\Leftrightarrow & x = \frac{131}{595} & & \\ & V = \left\{ \frac{131}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{3})& = & 2x+\frac{5}{7} \\\Leftrightarrow & 25x+\frac{10}{3}& = & 2x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+70} & = & \color{red}{42x} +15 \\\Leftrightarrow & 525x \color{red}{+70} \color{blue}{-70} \color{blue}{-42x} & = & \color{red}{42x} +15 \color{blue}{-42x} \color{blue}{-70} \\\Leftrightarrow & 525x-42x& = & 15-70 \\\Leftrightarrow & \color{red}{483} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{483} & & \\ & V = \left\{ \frac{-55}{483} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+50} & = & \color{red}{-54x} +81 \\\Leftrightarrow & -360x \color{red}{+50} \color{blue}{-50} \color{blue}{+54x} & = & \color{red}{-54x} +81 \color{blue}{+54x} \color{blue}{-50} \\\Leftrightarrow & -360x+54x& = & 81-50 \\\Leftrightarrow & \color{red}{-306} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-306} & & \\\Leftrightarrow & x = \frac{-31}{306} & & \\ & V = \left\{ \frac{-31}{306} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+12} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -140x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & -140x+98x& = & 35-12 \\\Leftrightarrow & \color{red}{-42} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-42} & & \\\Leftrightarrow & x = \frac{-23}{42} & & \\ & V = \left\{ \frac{-23}{42} \right\} & \\\end{align}\)
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