Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -24x+\frac{24}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x+ \frac{240}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{+240} & = & \color{red}{-550x} +99 \\\Leftrightarrow & -2640x \color{red}{+240} \color{blue}{-240} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{-240} \\\Leftrightarrow & -2640x+550x& = & 99-240 \\\Leftrightarrow & \color{red}{-2090} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-2090} & & \\\Leftrightarrow & x = \frac{141}{2090} & & \\ & V = \left\{ \frac{141}{2090} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{45x} +12 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-70} \\\Leftrightarrow & -210x-45x& = & 12-70 \\\Leftrightarrow & \color{red}{-255} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-255} & & \\\Leftrightarrow & x = \frac{58}{255} & & \\ & V = \left\{ \frac{58}{255} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & 6x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{126}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+30} & = & \color{red}{126x} +56 \\\Leftrightarrow & -525x \color{red}{+30} \color{blue}{-30} \color{blue}{-126x} & = & \color{red}{126x} +56 \color{blue}{-126x} \color{blue}{-30} \\\Leftrightarrow & -525x-126x& = & 56-30 \\\Leftrightarrow & \color{red}{-651} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-651} & & \\\Leftrightarrow & x = \frac{-26}{651} & & \\ & V = \left\{ \frac{-26}{651} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+216} & = & \color{red}{-315x} +40 \\\Leftrightarrow & -1350x \color{red}{+216} \color{blue}{-216} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-216} \\\Leftrightarrow & -1350x+315x& = & 40-216 \\\Leftrightarrow & \color{red}{-1035} x& = & -176 \\\Leftrightarrow & x = \frac{-176}{-1035} & & \\\Leftrightarrow & x = \frac{176}{1035} & & \\ & V = \left\{ \frac{176}{1035} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{9})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-35} & = & \color{red}{81x} +12 \\\Leftrightarrow & -315x \color{red}{-35} \color{blue}{+35} \color{blue}{-81x} & = & \color{red}{81x} +12 \color{blue}{-81x} \color{blue}{+35} \\\Leftrightarrow & -315x-81x& = & 12+35 \\\Leftrightarrow & \color{red}{-396} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-396} & & \\\Leftrightarrow & x = \frac{-47}{396} & & \\ & V = \left\{ \frac{-47}{396} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{35}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+385} & = & \color{red}{-264x} +18 \\\Leftrightarrow & -693x \color{red}{+385} \color{blue}{-385} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{-385} \\\Leftrightarrow & -693x+264x& = & 18-385 \\\Leftrightarrow & \color{red}{-429} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-429} & & \\\Leftrightarrow & x = \frac{367}{429} & & \\ & V = \left\{ \frac{367}{429} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{12}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+84} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -924x \color{red}{+84} \color{blue}{-84} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-84} \\\Leftrightarrow & -924x+385x& = & 22-84 \\\Leftrightarrow & \color{red}{-539} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-539} & & \\\Leftrightarrow & x = \frac{62}{539} & & \\ & V = \left\{ \frac{62}{539} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{231x} +88 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -198x-231x& = & 88+24 \\\Leftrightarrow & \color{red}{-429} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-429} & & \\\Leftrightarrow & x = \frac{-112}{429} & & \\ & V = \left\{ \frac{-112}{429} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{4})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{9}{4}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+45} & = & \color{red}{-80x} +24 \\\Leftrightarrow & 300x \color{red}{+45} \color{blue}{-45} \color{blue}{+80x} & = & \color{red}{-80x} +24 \color{blue}{+80x} \color{blue}{-45} \\\Leftrightarrow & 300x+80x& = & 24-45 \\\Leftrightarrow & \color{red}{380} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{380} & & \\ & V = \left\{ \frac{-21}{380} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -28x+\frac{21}{4}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-112}{ \color{blue}{4} }x+ \frac{21}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -112x \color{red}{+21} & = & \color{red}{32x} +18 \\\Leftrightarrow & -112x \color{red}{+21} \color{blue}{-21} \color{blue}{-32x} & = & \color{red}{32x} +18 \color{blue}{-32x} \color{blue}{-21} \\\Leftrightarrow & -112x-32x& = & 18-21 \\\Leftrightarrow & \color{red}{-144} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-144} & & \\\Leftrightarrow & x = \frac{1}{48} & & \\ & V = \left\{ \frac{1}{48} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 60x+25x& = & 8+12 \\\Leftrightarrow & \color{red}{85} x& = & 20 \\\Leftrightarrow & x = \frac{20}{85} & & \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x+\frac{6}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{+48} & = & \color{red}{440x} +99 \\\Leftrightarrow & 1056x \color{red}{+48} \color{blue}{-48} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{-48} \\\Leftrightarrow & 1056x-440x& = & 99-48 \\\Leftrightarrow & \color{red}{616} x& = & 51 \\\Leftrightarrow & x = \frac{51}{616} & & \\ & V = \left\{ \frac{51}{616} \right\} & \\\end{align}\)
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