Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{-135} & = & \color{red}{252x} +32 \\\Leftrightarrow & 324x \color{red}{-135} \color{blue}{+135} \color{blue}{-252x} & = & \color{red}{252x} +32 \color{blue}{-252x} \color{blue}{+135} \\\Leftrightarrow & 324x-252x& = & 32+135 \\\Leftrightarrow & \color{red}{72} x& = & 167 \\\Leftrightarrow & x = \frac{167}{72} & & \\ & V = \left\{ \frac{167}{72} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{12}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-36} & = & \color{red}{63x} +56 \\\Leftrightarrow & 420x \color{red}{-36} \color{blue}{+36} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{+36} \\\Leftrightarrow & 420x-63x& = & 56+36 \\\Leftrightarrow & \color{red}{357} x& = & 92 \\\Leftrightarrow & x = \frac{92}{357} & & \\ & V = \left\{ \frac{92}{357} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{-315x} +10 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -1350x+315x& = & 10-108 \\\Leftrightarrow & \color{red}{-1035} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-1035} & & \\\Leftrightarrow & x = \frac{98}{1035} & & \\ & V = \left\{ \frac{98}{1035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{-81x} +30 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{+81x} & = & \color{red}{-81x} +30 \color{blue}{+81x} \color{blue}{-28} \\\Leftrightarrow & 252x+81x& = & 30-28 \\\Leftrightarrow & \color{red}{333} x& = & 2 \\\Leftrightarrow & x = \frac{2}{333} & & \\ & V = \left\{ \frac{2}{333} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{8})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{25}{8}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{75}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+75} & = & \color{red}{168x} +32 \\\Leftrightarrow & -240x \color{red}{+75} \color{blue}{-75} \color{blue}{-168x} & = & \color{red}{168x} +32 \color{blue}{-168x} \color{blue}{-75} \\\Leftrightarrow & -240x-168x& = & 32-75 \\\Leftrightarrow & \color{red}{-408} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-408} & & \\\Leftrightarrow & x = \frac{43}{408} & & \\ & V = \left\{ \frac{43}{408} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 10x+\frac{6}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+66} & = & \color{red}{-165x} +25 \\\Leftrightarrow & 550x \color{red}{+66} \color{blue}{-66} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{-66} \\\Leftrightarrow & 550x+165x& = & 25-66 \\\Leftrightarrow & \color{red}{715} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{715} & & \\ & V = \left\{ \frac{-41}{715} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+16} & = & \color{red}{-54x} +81 \\\Leftrightarrow & 180x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +81 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 180x+54x& = & 81-16 \\\Leftrightarrow & \color{red}{234} x& = & 65 \\\Leftrightarrow & x = \frac{65}{234} & & \\\Leftrightarrow & x = \frac{5}{18} & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-90} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -396x \color{red}{-90} \color{blue}{+90} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+90} \\\Leftrightarrow & -396x+165x& = & 88+90 \\\Leftrightarrow & \color{red}{-231} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-231} & & \\\Leftrightarrow & x = \frac{-178}{231} & & \\ & V = \left\{ \frac{-178}{231} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{3})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 14x+\frac{35}{3}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{70}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+70} & = & \color{red}{-54x} +5 \\\Leftrightarrow & 84x \color{red}{+70} \color{blue}{-70} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-70} \\\Leftrightarrow & 84x+54x& = & 5-70 \\\Leftrightarrow & \color{red}{138} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{138} & & \\ & V = \left\{ \frac{-65}{138} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -9x+\frac{15}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-198}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -198x \color{red}{+30} & = & \color{red}{110x} +99 \\\Leftrightarrow & -198x \color{red}{+30} \color{blue}{-30} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-30} \\\Leftrightarrow & -198x-110x& = & 99-30 \\\Leftrightarrow & \color{red}{-308} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-308} & & \\\Leftrightarrow & x = \frac{-69}{308} & & \\ & V = \left\{ \frac{-69}{308} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{+24} & = & \color{red}{70x} +25 \\\Leftrightarrow & -160x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -160x-70x& = & 25-24 \\\Leftrightarrow & \color{red}{-230} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-230} & & \\\Leftrightarrow & x = \frac{-1}{230} & & \\ & V = \left\{ \frac{-1}{230} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{+154} & = & \color{red}{-495x} +30 \\\Leftrightarrow & 770x \color{red}{+154} \color{blue}{-154} \color{blue}{+495x} & = & \color{red}{-495x} +30 \color{blue}{+495x} \color{blue}{-154} \\\Leftrightarrow & 770x+495x& = & 30-154 \\\Leftrightarrow & \color{red}{1265} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{1265} & & \\ & V = \left\{ \frac{-124}{1265} \right\} & \\\end{align}\)
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