Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 80x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 80x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{105} x& = & 18 \\\Leftrightarrow & x = \frac{18}{105} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 10-36 \\\Leftrightarrow & \color{red}{255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{255} & & \\ & V = \left\{ \frac{-26}{255} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{4}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{135x} +10 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{+12} \\\Leftrightarrow & -120x-135x& = & 10+12 \\\Leftrightarrow & \color{red}{-255} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-255} & & \\\Leftrightarrow & x = \frac{-22}{255} & & \\ & V = \left\{ \frac{-22}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{105x} +50 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & -280x-105x& = & 50-84 \\\Leftrightarrow & \color{red}{-385} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-385} & & \\\Leftrightarrow & x = \frac{34}{385} & & \\ & V = \left\{ \frac{34}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 6x+\frac{3}{8} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 6x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-112} & = & \color{red}{144x} +9 \\\Leftrightarrow & -840x \color{red}{-112} \color{blue}{+112} \color{blue}{-144x} & = & \color{red}{144x} +9 \color{blue}{-144x} \color{blue}{+112} \\\Leftrightarrow & -840x-144x& = & 9+112 \\\Leftrightarrow & \color{red}{-984} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-984} & & \\\Leftrightarrow & x = \frac{-121}{984} & & \\ & V = \left\{ \frac{-121}{984} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{-440x} +30 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{+440x} & = & \color{red}{-440x} +30 \color{blue}{+440x} \color{blue}{-66} \\\Leftrightarrow & -825x+440x& = & 30-66 \\\Leftrightarrow & \color{red}{-385} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-385} & & \\\Leftrightarrow & x = \frac{36}{385} & & \\ & V = \left\{ \frac{36}{385} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2376}{ \color{blue}{132} }x+ \frac{288}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2376x \color{red}{+288} & = & \color{red}{660x} +55 \\\Leftrightarrow & 2376x \color{red}{+288} \color{blue}{-288} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{-288} \\\Leftrightarrow & 2376x-660x& = & 55-288 \\\Leftrightarrow & \color{red}{1716} x& = & -233 \\\Leftrightarrow & x = \frac{-233}{1716} & & \\ & V = \left\{ \frac{-233}{1716} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -25x+\frac{20}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2750}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2750x \color{red}{+200} & = & \color{red}{770x} +33 \\\Leftrightarrow & -2750x \color{red}{+200} \color{blue}{-200} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{-200} \\\Leftrightarrow & -2750x-770x& = & 33-200 \\\Leftrightarrow & \color{red}{-3520} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-3520} & & \\\Leftrightarrow & x = \frac{167}{3520} & & \\ & V = \left\{ \frac{167}{3520} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{96}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 96x \color{red}{+64} & = & \color{red}{-216x} +21 \\\Leftrightarrow & 96x \color{red}{+64} \color{blue}{-64} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{-64} \\\Leftrightarrow & 96x+216x& = & 21-64 \\\Leftrightarrow & \color{red}{312} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{312} & & \\ & V = \left\{ \frac{-43}{312} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & -4x+\frac{3}{11} \\\Leftrightarrow & 35x-\frac{21}{4}& = & -4x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1540}{ \color{blue}{44} }x- \frac{231}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1540x \color{red}{-231} & = & \color{red}{-176x} +12 \\\Leftrightarrow & 1540x \color{red}{-231} \color{blue}{+231} \color{blue}{+176x} & = & \color{red}{-176x} +12 \color{blue}{+176x} \color{blue}{+231} \\\Leftrightarrow & 1540x+176x& = & 12+231 \\\Leftrightarrow & \color{red}{1716} x& = & 243 \\\Leftrightarrow & x = \frac{243}{1716} & & \\\Leftrightarrow & x = \frac{81}{572} & & \\ & V = \left\{ \frac{81}{572} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+24} & = & \color{red}{77x} +10 \\\Leftrightarrow & 330x \color{red}{+24} \color{blue}{-24} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{-24} \\\Leftrightarrow & 330x-77x& = & 10-24 \\\Leftrightarrow & \color{red}{253} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{253} & & \\ & V = \left\{ \frac{-14}{253} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{-216} & = & \color{red}{693x} +55 \\\Leftrightarrow & -2970x \color{red}{-216} \color{blue}{+216} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{+216} \\\Leftrightarrow & -2970x-693x& = & 55+216 \\\Leftrightarrow & \color{red}{-3663} x& = & 271 \\\Leftrightarrow & x = \frac{271}{-3663} & & \\\Leftrightarrow & x = \frac{-271}{3663} & & \\ & V = \left\{ \frac{-271}{3663} \right\} & \\\end{align}\)
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