Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{15}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+75} & = & \color{red}{385x} +88 \\\Leftrightarrow & 550x \color{red}{+75} \color{blue}{-75} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{-75} \\\Leftrightarrow & 550x-385x& = & 88-75 \\\Leftrightarrow & \color{red}{165} x& = & 13 \\\Leftrightarrow & x = \frac{13}{165} & & \\ & V = \left\{ \frac{13}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 6x-\frac{4}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{20}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-20} & = & \color{red}{175x} +56 \\\Leftrightarrow & 210x \color{red}{-20} \color{blue}{+20} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{+20} \\\Leftrightarrow & 210x-175x& = & 56+20 \\\Leftrightarrow & \color{red}{35} x& = & 76 \\\Leftrightarrow & x = \frac{76}{35} & & \\ & V = \left\{ \frac{76}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{10}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-10} & = & \color{red}{9x} +2 \\\Leftrightarrow & -24x \color{red}{-10} \color{blue}{+10} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{+10} \\\Leftrightarrow & -24x-9x& = & 2+10 \\\Leftrightarrow & \color{red}{-33} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-33} & & \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{11})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x-\frac{28}{11}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1155}{ \color{blue}{55} }x- \frac{140}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1155x \color{red}{-140} & = & \color{red}{440x} +22 \\\Leftrightarrow & -1155x \color{red}{-140} \color{blue}{+140} \color{blue}{-440x} & = & \color{red}{440x} +22 \color{blue}{-440x} \color{blue}{+140} \\\Leftrightarrow & -1155x-440x& = & 22+140 \\\Leftrightarrow & \color{red}{-1595} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-1595} & & \\\Leftrightarrow & x = \frac{-162}{1595} & & \\ & V = \left\{ \frac{-162}{1595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+6} & = & \color{red}{55x} +4 \\\Leftrightarrow & -44x \color{red}{+6} \color{blue}{-6} \color{blue}{-55x} & = & \color{red}{55x} +4 \color{blue}{-55x} \color{blue}{-6} \\\Leftrightarrow & -44x-55x& = & 4-6 \\\Leftrightarrow & \color{red}{-99} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-99} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 1650x+385x& = & 50-132 \\\Leftrightarrow & \color{red}{2035} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{2035} & & \\ & V = \left\{ \frac{-82}{2035} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -8x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+54} & = & \color{red}{-504x} +14 \\\Leftrightarrow & -945x \color{red}{+54} \color{blue}{-54} \color{blue}{+504x} & = & \color{red}{-504x} +14 \color{blue}{+504x} \color{blue}{-54} \\\Leftrightarrow & -945x+504x& = & 14-54 \\\Leftrightarrow & \color{red}{-441} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-441} & & \\\Leftrightarrow & x = \frac{40}{441} & & \\ & V = \left\{ \frac{40}{441} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{11})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 28x-\frac{14}{11}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x- \frac{14}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{-14} & = & \color{red}{-33x} +5 \\\Leftrightarrow & 308x \color{red}{-14} \color{blue}{+14} \color{blue}{+33x} & = & \color{red}{-33x} +5 \color{blue}{+33x} \color{blue}{+14} \\\Leftrightarrow & 308x+33x& = & 5+14 \\\Leftrightarrow & \color{red}{341} x& = & 19 \\\Leftrightarrow & x = \frac{19}{341} & & \\ & V = \left\{ \frac{19}{341} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+14} & = & \color{red}{-15x} +6 \\\Leftrightarrow & -70x \color{red}{+14} \color{blue}{-14} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{-14} \\\Leftrightarrow & -70x+15x& = & 6-14 \\\Leftrightarrow & \color{red}{-55} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-55} & & \\\Leftrightarrow & x = \frac{8}{55} & & \\ & V = \left\{ \frac{8}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{120x} +50 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{-120x} & = & \color{red}{120x} +50 \color{blue}{-120x} \color{blue}{+36} \\\Leftrightarrow & -225x-120x& = & 50+36 \\\Leftrightarrow & \color{red}{-345} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-345} & & \\\Leftrightarrow & x = \frac{-86}{345} & & \\ & V = \left\{ \frac{-86}{345} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-30} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 550x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & 550x+385x& = & 22+30 \\\Leftrightarrow & \color{red}{935} x& = & 52 \\\Leftrightarrow & x = \frac{52}{935} & & \\ & V = \left\{ \frac{52}{935} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{35}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+35} & = & \color{red}{27x} +8 \\\Leftrightarrow & 105x \color{red}{+35} \color{blue}{-35} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-35} \\\Leftrightarrow & 105x-27x& = & 8-35 \\\Leftrightarrow & \color{red}{78} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{78} & & \\\Leftrightarrow & x = \frac{-9}{26} & & \\ & V = \left\{ \frac{-9}{26} \right\} & \\\end{align}\)
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