Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-56} & = & \color{red}{-189x} +90 \\\Leftrightarrow & -504x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & -504x+189x& = & 90+56 \\\Leftrightarrow & \color{red}{-315} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-315} & & \\\Leftrightarrow & x = \frac{-146}{315} & & \\ & V = \left\{ \frac{-146}{315} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-275x} +44 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -1320x+275x& = & 44+90 \\\Leftrightarrow & \color{red}{-1045} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-1045} & & \\\Leftrightarrow & x = \frac{-134}{1045} & & \\ & V = \left\{ \frac{-134}{1045} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{+135} & = & \color{red}{180x} +20 \\\Leftrightarrow & 432x \color{red}{+135} \color{blue}{-135} \color{blue}{-180x} & = & \color{red}{180x} +20 \color{blue}{-180x} \color{blue}{-135} \\\Leftrightarrow & 432x-180x& = & 20-135 \\\Leftrightarrow & \color{red}{252} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{252} & & \\ & V = \left\{ \frac{-115}{252} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{10}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+20} & = & \color{red}{54x} +9 \\\Leftrightarrow & -48x \color{red}{+20} \color{blue}{-20} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-20} \\\Leftrightarrow & -48x-54x& = & 9-20 \\\Leftrightarrow & \color{red}{-102} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-102} & & \\\Leftrightarrow & x = \frac{11}{102} & & \\ & V = \left\{ \frac{11}{102} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{147x} +28 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & 126x-147x& = & 28-18 \\\Leftrightarrow & \color{red}{-21} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-21} & & \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1320}{ \color{blue}{132} }x- \frac{120}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1320x \color{red}{-120} & = & \color{red}{924x} +77 \\\Leftrightarrow & -1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-924x} & = & \color{red}{924x} +77 \color{blue}{-924x} \color{blue}{+120} \\\Leftrightarrow & -1320x-924x& = & 77+120 \\\Leftrightarrow & \color{red}{-2244} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-2244} & & \\\Leftrightarrow & x = \frac{-197}{2244} & & \\ & V = \left\{ \frac{-197}{2244} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+60} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -90x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & -90x+63x& = & 2-60 \\\Leftrightarrow & \color{red}{-27} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-27} & & \\\Leftrightarrow & x = \frac{58}{27} & & \\ & V = \left\{ \frac{58}{27} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-162} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -1782x \color{red}{-162} \color{blue}{+162} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+162} \\\Leftrightarrow & -1782x+297x& = & 44+162 \\\Leftrightarrow & \color{red}{-1485} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-1485} & & \\\Leftrightarrow & x = \frac{-206}{1485} & & \\ & V = \left\{ \frac{-206}{1485} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+66} & = & \color{red}{495x} +25 \\\Leftrightarrow & -440x \color{red}{+66} \color{blue}{-66} \color{blue}{-495x} & = & \color{red}{495x} +25 \color{blue}{-495x} \color{blue}{-66} \\\Leftrightarrow & -440x-495x& = & 25-66 \\\Leftrightarrow & \color{red}{-935} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-935} & & \\\Leftrightarrow & x = \frac{41}{935} & & \\ & V = \left\{ \frac{41}{935} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{3})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -20x+\frac{16}{3}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+176} & = & \color{red}{-231x} +12 \\\Leftrightarrow & -660x \color{red}{+176} \color{blue}{-176} \color{blue}{+231x} & = & \color{red}{-231x} +12 \color{blue}{+231x} \color{blue}{-176} \\\Leftrightarrow & -660x+231x& = & 12-176 \\\Leftrightarrow & \color{red}{-429} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{-429} & & \\\Leftrightarrow & x = \frac{164}{429} & & \\ & V = \left\{ \frac{164}{429} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 28x-\frac{35}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x- \frac{140}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{-140} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 1232x \color{red}{-140} \color{blue}{+140} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+140} \\\Leftrightarrow & 1232x+220x& = & 99+140 \\\Leftrightarrow & \color{red}{1452} x& = & 239 \\\Leftrightarrow & x = \frac{239}{1452} & & \\ & V = \left\{ \frac{239}{1452} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{8})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+75} & = & \color{red}{-280x} +72 \\\Leftrightarrow & 600x \color{red}{+75} \color{blue}{-75} \color{blue}{+280x} & = & \color{red}{-280x} +72 \color{blue}{+280x} \color{blue}{-75} \\\Leftrightarrow & 600x+280x& = & 72-75 \\\Leftrightarrow & \color{red}{880} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{880} & & \\ & V = \left\{ \frac{-3}{880} \right\} & \\\end{align}\)
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