Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{+88} & = & \color{red}{495x} +81 \\\Leftrightarrow & 1584x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +81 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & 1584x-495x& = & 81-88 \\\Leftrightarrow & \color{red}{1089} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{1089} & & \\ & V = \left\{ \frac{-7}{1089} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{15}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+105} & = & \color{red}{385x} +99 \\\Leftrightarrow & 924x \color{red}{+105} \color{blue}{-105} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{-105} \\\Leftrightarrow & 924x-385x& = & 99-105 \\\Leftrightarrow & \color{red}{539} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{539} & & \\ & V = \left\{ \frac{-6}{539} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{105x} +40 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 120x-105x& = & 40+36 \\\Leftrightarrow & \color{red}{15} x& = & 76 \\\Leftrightarrow & x = \frac{76}{15} & & \\ & V = \left\{ \frac{76}{15} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-245x} +30 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 420x+245x& = & 30-84 \\\Leftrightarrow & \color{red}{665} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{665} & & \\ & V = \left\{ \frac{-54}{665} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & -132x+55x& = & 6-24 \\\Leftrightarrow & \color{red}{-77} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-77} & & \\\Leftrightarrow & x = \frac{18}{77} & & \\ & V = \left\{ \frac{18}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{132x} +99 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{-132x} & = & \color{red}{132x} +99 \color{blue}{-132x} \color{blue}{+40} \\\Leftrightarrow & 440x-132x& = & 99+40 \\\Leftrightarrow & \color{red}{308} x& = & 139 \\\Leftrightarrow & x = \frac{139}{308} & & \\ & V = \left\{ \frac{139}{308} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 18x-\frac{12}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{-12} & = & \color{red}{35x} +2 \\\Leftrightarrow & 126x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 126x-35x& = & 2+12 \\\Leftrightarrow & \color{red}{91} x& = & 14 \\\Leftrightarrow & x = \frac{14}{91} & & \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-132} & = & \color{red}{275x} +40 \\\Leftrightarrow & 330x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 330x-275x& = & 40+132 \\\Leftrightarrow & \color{red}{55} x& = & 172 \\\Leftrightarrow & x = \frac{172}{55} & & \\ & V = \left\{ \frac{172}{55} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{10}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+20} & = & \color{red}{154x} +99 \\\Leftrightarrow & -132x \color{red}{+20} \color{blue}{-20} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-20} \\\Leftrightarrow & -132x-154x& = & 99-20 \\\Leftrightarrow & \color{red}{-286} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-286} & & \\\Leftrightarrow & x = \frac{-79}{286} & & \\ & V = \left\{ \frac{-79}{286} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{35x} +10 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 168x-35x& = & 10-30 \\\Leftrightarrow & \color{red}{133} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{133} & & \\ & V = \left\{ \frac{-20}{133} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{9})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-135}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -135x \color{red}{-20} & = & \color{red}{-72x} +12 \\\Leftrightarrow & -135x \color{red}{-20} \color{blue}{+20} \color{blue}{+72x} & = & \color{red}{-72x} +12 \color{blue}{+72x} \color{blue}{+20} \\\Leftrightarrow & -135x+72x& = & 12+20 \\\Leftrightarrow & \color{red}{-63} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-63} & & \\\Leftrightarrow & x = \frac{-32}{63} & & \\ & V = \left\{ \frac{-32}{63} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{4})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{25}{4}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x+ \frac{25}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{+25} & = & \color{red}{-28x} +6 \\\Leftrightarrow & 40x \color{red}{+25} \color{blue}{-25} \color{blue}{+28x} & = & \color{red}{-28x} +6 \color{blue}{+28x} \color{blue}{-25} \\\Leftrightarrow & 40x+28x& = & 6-25 \\\Leftrightarrow & \color{red}{68} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{68} & & \\ & V = \left\{ \frac{-19}{68} \right\} & \\\end{align}\)
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