Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{7})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{27}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-27} & = & \color{red}{105x} +49 \\\Leftrightarrow & -252x \color{red}{-27} \color{blue}{+27} \color{blue}{-105x} & = & \color{red}{105x} +49 \color{blue}{-105x} \color{blue}{+27} \\\Leftrightarrow & -252x-105x& = & 49+27 \\\Leftrightarrow & \color{red}{-357} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-357} & & \\\Leftrightarrow & x = \frac{-76}{357} & & \\ & V = \left\{ \frac{-76}{357} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & -8x+\frac{5}{8} \\\Leftrightarrow & -15x+\frac{20}{3}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{+160} & = & \color{red}{-192x} +15 \\\Leftrightarrow & -360x \color{red}{+160} \color{blue}{-160} \color{blue}{+192x} & = & \color{red}{-192x} +15 \color{blue}{+192x} \color{blue}{-160} \\\Leftrightarrow & -360x+192x& = & 15-160 \\\Leftrightarrow & \color{red}{-168} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-168} & & \\\Leftrightarrow & x = \frac{145}{168} & & \\ & V = \left\{ \frac{145}{168} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & -6x+\frac{10}{11} \\\Leftrightarrow & -28x-\frac{35}{3}& = & -6x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-385} & = & \color{red}{-198x} +30 \\\Leftrightarrow & -924x \color{red}{-385} \color{blue}{+385} \color{blue}{+198x} & = & \color{red}{-198x} +30 \color{blue}{+198x} \color{blue}{+385} \\\Leftrightarrow & -924x+198x& = & 30+385 \\\Leftrightarrow & \color{red}{-726} x& = & 415 \\\Leftrightarrow & x = \frac{415}{-726} & & \\\Leftrightarrow & x = \frac{-415}{726} & & \\ & V = \left\{ \frac{-415}{726} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{25}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{75}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+75} & = & \color{red}{189x} +28 \\\Leftrightarrow & 525x \color{red}{+75} \color{blue}{-75} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-75} \\\Leftrightarrow & 525x-189x& = & 28-75 \\\Leftrightarrow & \color{red}{336} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{336} & & \\ & V = \left\{ \frac{-47}{336} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 120x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{95} x& = & 18 \\\Leftrightarrow & x = \frac{18}{95} & & \\ & V = \left\{ \frac{18}{95} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 180x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{105} x& = & 4 \\\Leftrightarrow & x = \frac{4}{105} & & \\ & V = \left\{ \frac{4}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+36} & = & \color{red}{-105x} +25 \\\Leftrightarrow & 450x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +25 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 450x+105x& = & 25-36 \\\Leftrightarrow & \color{red}{555} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{555} & & \\ & V = \left\{ \frac{-11}{555} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{8})& = & -2x+\frac{3}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -2x+\frac{3}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-176}{ \color{blue}{88} }x+ \frac{24}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-176x} +24 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +24 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & 1320x+176x& = & 24-165 \\\Leftrightarrow & \color{red}{1496} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{1496} & & \\ & V = \left\{ \frac{-141}{1496} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{2})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 20x+\frac{15}{2}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{60}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+60} & = & \color{red}{56x} +7 \\\Leftrightarrow & 160x \color{red}{+60} \color{blue}{-60} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{-60} \\\Leftrightarrow & 160x-56x& = & 7-60 \\\Leftrightarrow & \color{red}{104} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{104} & & \\ & V = \left\{ \frac{-53}{104} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{15}{2}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{24}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 24x \color{red}{-15} & = & \color{red}{-10x} +3 \\\Leftrightarrow & 24x \color{red}{-15} \color{blue}{+15} \color{blue}{+10x} & = & \color{red}{-10x} +3 \color{blue}{+10x} \color{blue}{+15} \\\Leftrightarrow & 24x+10x& = & 3+15 \\\Leftrightarrow & \color{red}{34} x& = & 18 \\\Leftrightarrow & x = \frac{18}{34} & & \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 14+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 284 \\\Leftrightarrow & x = \frac{284}{-1197} & & \\\Leftrightarrow & x = \frac{-284}{1197} & & \\ & V = \left\{ \frac{-284}{1197} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-72} & = & \color{red}{231x} +22 \\\Leftrightarrow & -990x \color{red}{-72} \color{blue}{+72} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+72} \\\Leftrightarrow & -990x-231x& = & 22+72 \\\Leftrightarrow & \color{red}{-1221} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-1221} & & \\\Leftrightarrow & x = \frac{-94}{1221} & & \\ & V = \left\{ \frac{-94}{1221} \right\} & \\\end{align}\)
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