Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{45x} +40 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{+18} \\\Leftrightarrow & 60x-45x& = & 40+18 \\\Leftrightarrow & \color{red}{15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{15} & & \\ & V = \left\{ \frac{58}{15} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{+196} & = & \color{red}{-189x} +12 \\\Leftrightarrow & 294x \color{red}{+196} \color{blue}{-196} \color{blue}{+189x} & = & \color{red}{-189x} +12 \color{blue}{+189x} \color{blue}{-196} \\\Leftrightarrow & 294x+189x& = & 12-196 \\\Leftrightarrow & \color{red}{483} x& = & -184 \\\Leftrightarrow & x = \frac{-184}{483} & & \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{16}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{165x} +44 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-48} \\\Leftrightarrow & 396x-165x& = & 44-48 \\\Leftrightarrow & \color{red}{231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{231} & & \\ & V = \left\{ \frac{-4}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -880x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -880x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{-495} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-495} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-108} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1980x \color{red}{-108} \color{blue}{+108} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+108} \\\Leftrightarrow & 1980x+693x& = & 110+108 \\\Leftrightarrow & \color{red}{2673} x& = & 218 \\\Leftrightarrow & x = \frac{218}{2673} & & \\ & V = \left\{ \frac{218}{2673} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{1}{2})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 14x-\frac{7}{2}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x- \frac{35}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{-35} & = & \color{red}{-50x} +8 \\\Leftrightarrow & 140x \color{red}{-35} \color{blue}{+35} \color{blue}{+50x} & = & \color{red}{-50x} +8 \color{blue}{+50x} \color{blue}{+35} \\\Leftrightarrow & 140x+50x& = & 8+35 \\\Leftrightarrow & \color{red}{190} x& = & 43 \\\Leftrightarrow & x = \frac{43}{190} & & \\ & V = \left\{ \frac{43}{190} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+264} & = & \color{red}{-385x} +20 \\\Leftrightarrow & 1650x \color{red}{+264} \color{blue}{-264} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{-264} \\\Leftrightarrow & 1650x+385x& = & 20-264 \\\Leftrightarrow & \color{red}{2035} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{2035} & & \\ & V = \left\{ \frac{-244}{2035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x-\frac{20}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-448}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -448x \color{red}{-80} & = & \color{red}{196x} +35 \\\Leftrightarrow & -448x \color{red}{-80} \color{blue}{+80} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{+80} \\\Leftrightarrow & -448x-196x& = & 35+80 \\\Leftrightarrow & \color{red}{-644} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-644} & & \\\Leftrightarrow & x = \frac{-5}{28} & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{-495x} +20 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{+495x} & = & \color{red}{-495x} +20 \color{blue}{+495x} \color{blue}{-132} \\\Leftrightarrow & 880x+495x& = & 20-132 \\\Leftrightarrow & \color{red}{1375} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{1375} & & \\ & V = \left\{ \frac{-112}{1375} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+220} & = & \color{red}{-385x} +14 \\\Leftrightarrow & -924x \color{red}{+220} \color{blue}{-220} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{-220} \\\Leftrightarrow & -924x+385x& = & 14-220 \\\Leftrightarrow & \color{red}{-539} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{-539} & & \\\Leftrightarrow & x = \frac{206}{539} & & \\ & V = \left\{ \frac{206}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 24x+\frac{18}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{105x} +70 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-54} \\\Leftrightarrow & 504x-105x& = & 70-54 \\\Leftrightarrow & \color{red}{399} x& = & 16 \\\Leftrightarrow & x = \frac{16}{399} & & \\ & V = \left\{ \frac{16}{399} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-270} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1890x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & -1890x+441x& = & 14+270 \\\Leftrightarrow & \color{red}{-1449} x& = & 284 \\\Leftrightarrow & x = \frac{284}{-1449} & & \\\Leftrightarrow & x = \frac{-284}{1449} & & \\ & V = \left\{ \frac{-284}{1449} \right\} & \\\end{align}\)
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