Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{3})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-42} & = & \color{red}{45x} +7 \\\Leftrightarrow & 126x \color{red}{-42} \color{blue}{+42} \color{blue}{-45x} & = & \color{red}{45x} +7 \color{blue}{-45x} \color{blue}{+42} \\\Leftrightarrow & 126x-45x& = & 7+42 \\\Leftrightarrow & \color{red}{81} x& = & 49 \\\Leftrightarrow & x = \frac{49}{81} & & \\ & V = \left\{ \frac{49}{81} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+36} \\\Leftrightarrow & 120x+70x& = & 45+36 \\\Leftrightarrow & \color{red}{190} x& = & 81 \\\Leftrightarrow & x = \frac{81}{190} & & \\ & V = \left\{ \frac{81}{190} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-30} & = & \color{red}{315x} +42 \\\Leftrightarrow & -280x \color{red}{-30} \color{blue}{+30} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+30} \\\Leftrightarrow & -280x-315x& = & 42+30 \\\Leftrightarrow & \color{red}{-595} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-595} & & \\\Leftrightarrow & x = \frac{-72}{595} & & \\ & V = \left\{ \frac{-72}{595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{1}{2})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{5}{2}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+25} & = & \color{red}{-70x} +8 \\\Leftrightarrow & 100x \color{red}{+25} \color{blue}{-25} \color{blue}{+70x} & = & \color{red}{-70x} +8 \color{blue}{+70x} \color{blue}{-25} \\\Leftrightarrow & 100x+70x& = & 8-25 \\\Leftrightarrow & \color{red}{170} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{170} & & \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{21x} +2 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -60x-21x& = & 2-8 \\\Leftrightarrow & \color{red}{-81} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-81} & & \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{2})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -14x+\frac{35}{2}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x+ \frac{385}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{+385} & = & \color{red}{-66x} +10 \\\Leftrightarrow & -308x \color{red}{+385} \color{blue}{-385} \color{blue}{+66x} & = & \color{red}{-66x} +10 \color{blue}{+66x} \color{blue}{-385} \\\Leftrightarrow & -308x+66x& = & 10-385 \\\Leftrightarrow & \color{red}{-242} x& = & -375 \\\Leftrightarrow & x = \frac{-375}{-242} & & \\\Leftrightarrow & x = \frac{375}{242} & & \\ & V = \left\{ \frac{375}{242} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{24}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+120} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 1650x \color{red}{+120} \color{blue}{-120} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-120} \\\Leftrightarrow & 1650x+385x& = & 66-120 \\\Leftrightarrow & \color{red}{2035} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{2035} & & \\ & V = \left\{ \frac{-54}{2035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{70x} +35 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -60x-70x& = & 35+12 \\\Leftrightarrow & \color{red}{-130} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-130} & & \\\Leftrightarrow & x = \frac{-47}{130} & & \\ & V = \left\{ \frac{-47}{130} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 24x-\frac{24}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{25x} +2 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 120x-25x& = & 2+24 \\\Leftrightarrow & \color{red}{95} x& = & 26 \\\Leftrightarrow & x = \frac{26}{95} & & \\ & V = \left\{ \frac{26}{95} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{8})& = & -4x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{-224x} +48 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{+224x} & = & \color{red}{-224x} +48 \color{blue}{+224x} \color{blue}{+147} \\\Leftrightarrow & 1176x+224x& = & 48+147 \\\Leftrightarrow & \color{red}{1400} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1400} & & \\\Leftrightarrow & x = \frac{39}{280} & & \\ & V = \left\{ \frac{39}{280} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{28}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+140} & = & \color{red}{135x} +18 \\\Leftrightarrow & -525x \color{red}{+140} \color{blue}{-140} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{-140} \\\Leftrightarrow & -525x-135x& = & 18-140 \\\Leftrightarrow & \color{red}{-660} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-660} & & \\\Leftrightarrow & x = \frac{61}{330} & & \\ & V = \left\{ \frac{61}{330} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -18x+\frac{18}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+54} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -270x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & -270x+105x& = & 10-54 \\\Leftrightarrow & \color{red}{-165} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-165} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
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