Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-20} & = & \color{red}{9x} +4 \\\Leftrightarrow & 60x \color{red}{-20} \color{blue}{+20} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{+20} \\\Leftrightarrow & 60x-9x& = & 4+20 \\\Leftrightarrow & \color{red}{51} x& = & 24 \\\Leftrightarrow & x = \frac{24}{51} & & \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{-216} & = & \color{red}{225x} +20 \\\Leftrightarrow & -1080x \color{red}{-216} \color{blue}{+216} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{+216} \\\Leftrightarrow & -1080x-225x& = & 20+216 \\\Leftrightarrow & \color{red}{-1305} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1305} & & \\\Leftrightarrow & x = \frac{-236}{1305} & & \\ & V = \left\{ \frac{-236}{1305} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+12} & = & \color{red}{-99x} +10 \\\Leftrightarrow & -88x \color{red}{+12} \color{blue}{-12} \color{blue}{+99x} & = & \color{red}{-99x} +10 \color{blue}{+99x} \color{blue}{-12} \\\Leftrightarrow & -88x+99x& = & 10-12 \\\Leftrightarrow & \color{red}{11} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x-\frac{24}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-216} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -1890x \color{red}{-216} \color{blue}{+216} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{+216} \\\Leftrightarrow & -1890x+441x& = & 28+216 \\\Leftrightarrow & \color{red}{-1449} x& = & 244 \\\Leftrightarrow & x = \frac{244}{-1449} & & \\\Leftrightarrow & x = \frac{-244}{1449} & & \\ & V = \left\{ \frac{-244}{1449} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{-385x} +25 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{+264} \\\Leftrightarrow & 1650x+385x& = & 25+264 \\\Leftrightarrow & \color{red}{2035} x& = & 289 \\\Leftrightarrow & x = \frac{289}{2035} & & \\ & V = \left\{ \frac{289}{2035} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-154} & = & \color{red}{-297x} +6 \\\Leftrightarrow & 462x \color{red}{-154} \color{blue}{+154} \color{blue}{+297x} & = & \color{red}{-297x} +6 \color{blue}{+297x} \color{blue}{+154} \\\Leftrightarrow & 462x+297x& = & 6+154 \\\Leftrightarrow & \color{red}{759} x& = & 160 \\\Leftrightarrow & x = \frac{160}{759} & & \\ & V = \left\{ \frac{160}{759} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+45} & = & \color{red}{-120x} +80 \\\Leftrightarrow & 288x \color{red}{+45} \color{blue}{-45} \color{blue}{+120x} & = & \color{red}{-120x} +80 \color{blue}{+120x} \color{blue}{-45} \\\Leftrightarrow & 288x+120x& = & 80-45 \\\Leftrightarrow & \color{red}{408} x& = & 35 \\\Leftrightarrow & x = \frac{35}{408} & & \\ & V = \left\{ \frac{35}{408} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 6x+\frac{10}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+70} & = & \color{red}{147x} +18 \\\Leftrightarrow & 126x \color{red}{+70} \color{blue}{-70} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{-70} \\\Leftrightarrow & 126x-147x& = & 18-70 \\\Leftrightarrow & \color{red}{-21} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-21} & & \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{6})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -14x+\frac{35}{6}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-588}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -588x \color{red}{+245} & = & \color{red}{-210x} +36 \\\Leftrightarrow & -588x \color{red}{+245} \color{blue}{-245} \color{blue}{+210x} & = & \color{red}{-210x} +36 \color{blue}{+210x} \color{blue}{-245} \\\Leftrightarrow & -588x+210x& = & 36-245 \\\Leftrightarrow & \color{red}{-378} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{-378} & & \\\Leftrightarrow & x = \frac{209}{378} & & \\ & V = \left\{ \frac{209}{378} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{4}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+20} & = & \color{red}{245x} +14 \\\Leftrightarrow & -210x \color{red}{+20} \color{blue}{-20} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-20} \\\Leftrightarrow & -210x-245x& = & 14-20 \\\Leftrightarrow & \color{red}{-455} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-455} & & \\\Leftrightarrow & x = \frac{6}{455} & & \\ & V = \left\{ \frac{6}{455} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{6}{5}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-18} & = & \color{red}{30x} +40 \\\Leftrightarrow & 135x \color{red}{-18} \color{blue}{+18} \color{blue}{-30x} & = & \color{red}{30x} +40 \color{blue}{-30x} \color{blue}{+18} \\\Leftrightarrow & 135x-30x& = & 40+18 \\\Leftrightarrow & \color{red}{105} x& = & 58 \\\Leftrightarrow & x = \frac{58}{105} & & \\ & V = \left\{ \frac{58}{105} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 4x+\frac{4}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{+4} & = & \color{red}{33x} +6 \\\Leftrightarrow & 44x \color{red}{+4} \color{blue}{-4} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{-4} \\\Leftrightarrow & 44x-33x& = & 6-4 \\\Leftrightarrow & \color{red}{11} x& = & 2 \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
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