Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{16}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+48} & = & \color{red}{147x} +14 \\\Leftrightarrow & 420x \color{red}{+48} \color{blue}{-48} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-48} \\\Leftrightarrow & 420x-147x& = & 14-48 \\\Leftrightarrow & \color{red}{273} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{273} & & \\ & V = \left\{ \frac{-34}{273} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 330x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 330x+275x& = & 30+132 \\\Leftrightarrow & \color{red}{605} x& = & 162 \\\Leftrightarrow & x = \frac{162}{605} & & \\ & V = \left\{ \frac{162}{605} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{24}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-72} & = & \color{red}{231x} +110 \\\Leftrightarrow & 990x \color{red}{-72} \color{blue}{+72} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+72} \\\Leftrightarrow & 990x-231x& = & 110+72 \\\Leftrightarrow & \color{red}{759} x& = & 182 \\\Leftrightarrow & x = \frac{182}{759} & & \\ & V = \left\{ \frac{182}{759} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{-126x} +49 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{+40} \\\Leftrightarrow & 280x+126x& = & 49+40 \\\Leftrightarrow & \color{red}{406} x& = & 89 \\\Leftrightarrow & x = \frac{89}{406} & & \\ & V = \left\{ \frac{89}{406} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{3})& = & -4x+\frac{7}{4} \\\Leftrightarrow & 35x-\frac{35}{3}& = & -4x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{-48x} +21 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{+48x} & = & \color{red}{-48x} +21 \color{blue}{+48x} \color{blue}{+140} \\\Leftrightarrow & 420x+48x& = & 21+140 \\\Leftrightarrow & \color{red}{468} x& = & 161 \\\Leftrightarrow & x = \frac{161}{468} & & \\ & V = \left\{ \frac{161}{468} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & -9x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1320}{ \color{blue}{132} }x- \frac{120}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{-1188x} +55 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{+1188x} & = & \color{red}{-1188x} +55 \color{blue}{+1188x} \color{blue}{+120} \\\Leftrightarrow & 1320x+1188x& = & 55+120 \\\Leftrightarrow & \color{red}{2508} x& = & 175 \\\Leftrightarrow & x = \frac{175}{2508} & & \\ & V = \left\{ \frac{175}{2508} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{-264x} +64 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +64 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & -1232x+264x& = & 64+231 \\\Leftrightarrow & \color{red}{-968} x& = & 295 \\\Leftrightarrow & x = \frac{295}{-968} & & \\\Leftrightarrow & x = \frac{-295}{968} & & \\ & V = \left\{ \frac{-295}{968} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{4})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -12x+\frac{9}{4}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{140x} +36 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{-140x} & = & \color{red}{140x} +36 \color{blue}{-140x} \color{blue}{-63} \\\Leftrightarrow & -336x-140x& = & 36-63 \\\Leftrightarrow & \color{red}{-476} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-476} & & \\\Leftrightarrow & x = \frac{27}{476} & & \\ & V = \left\{ \frac{27}{476} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+220} & = & \color{red}{385x} +28 \\\Leftrightarrow & 924x \color{red}{+220} \color{blue}{-220} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-220} \\\Leftrightarrow & 924x-385x& = & 28-220 \\\Leftrightarrow & \color{red}{539} x& = & -192 \\\Leftrightarrow & x = \frac{-192}{539} & & \\ & V = \left\{ \frac{-192}{539} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 14x-\frac{35}{2}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{315}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-315} & = & \color{red}{162x} +8 \\\Leftrightarrow & 252x \color{red}{-315} \color{blue}{+315} \color{blue}{-162x} & = & \color{red}{162x} +8 \color{blue}{-162x} \color{blue}{+315} \\\Leftrightarrow & 252x-162x& = & 8+315 \\\Leftrightarrow & \color{red}{90} x& = & 323 \\\Leftrightarrow & x = \frac{323}{90} & & \\ & V = \left\{ \frac{323}{90} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{6}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-6} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-6} \color{blue}{+6} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+6} \\\Leftrightarrow & 60x+25x& = & 6+6 \\\Leftrightarrow & \color{red}{85} x& = & 12 \\\Leftrightarrow & x = \frac{12}{85} & & \\ & V = \left\{ \frac{12}{85} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{3})& = & 9x+\frac{5}{7} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 9x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{189x} +15 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +15 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & 84x-189x& = & 15-56 \\\Leftrightarrow & \color{red}{-105} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-105} & & \\\Leftrightarrow & x = \frac{41}{105} & & \\ & V = \left\{ \frac{41}{105} \right\} & \\\end{align}\)
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