Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{7})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{9}{7}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{27}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-27} & = & \color{red}{168x} +56 \\\Leftrightarrow & -315x \color{red}{-27} \color{blue}{+27} \color{blue}{-168x} & = & \color{red}{168x} +56 \color{blue}{-168x} \color{blue}{+27} \\\Leftrightarrow & -315x-168x& = & 56+27 \\\Leftrightarrow & \color{red}{-483} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-483} & & \\\Leftrightarrow & x = \frac{-83}{483} & & \\ & V = \left\{ \frac{-83}{483} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+132} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 924x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 924x+385x& = & 42-132 \\\Leftrightarrow & \color{red}{1309} x& = & -90 \\\Leftrightarrow & x = \frac{-90}{1309} & & \\ & V = \left\{ \frac{-90}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{4})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{25}{4}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{75}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{-84x} +16 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{+84x} & = & \color{red}{-84x} +16 \color{blue}{+84x} \color{blue}{-75} \\\Leftrightarrow & -120x+84x& = & 16-75 \\\Leftrightarrow & \color{red}{-36} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-36} & & \\\Leftrightarrow & x = \frac{59}{36} & & \\ & V = \left\{ \frac{59}{36} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{-60x} +21 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{+60x} & = & \color{red}{-60x} +21 \color{blue}{+60x} \color{blue}{-56} \\\Leftrightarrow & 168x+60x& = & 21-56 \\\Leftrightarrow & \color{red}{228} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{228} & & \\ & V = \left\{ \frac{-35}{228} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-18} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 168x \color{red}{-18} \color{blue}{+18} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+18} \\\Leftrightarrow & 168x+189x& = & 70+18 \\\Leftrightarrow & \color{red}{357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{357} & & \\ & V = \left\{ \frac{88}{357} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{600}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 600x \color{red}{-48} & = & \color{red}{-140x} +15 \\\Leftrightarrow & 600x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & 600x+140x& = & 15+48 \\\Leftrightarrow & \color{red}{740} x& = & 63 \\\Leftrightarrow & x = \frac{63}{740} & & \\ & V = \left\{ \frac{63}{740} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-60} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 336x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & 336x+147x& = & 14+60 \\\Leftrightarrow & \color{red}{483} x& = & 74 \\\Leftrightarrow & x = \frac{74}{483} & & \\ & V = \left\{ \frac{74}{483} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{3})& = & -6x+\frac{5}{9} \\\Leftrightarrow & 35x-\frac{35}{3}& = & -6x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x- \frac{105}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{-105} & = & \color{red}{-54x} +5 \\\Leftrightarrow & 315x \color{red}{-105} \color{blue}{+105} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{+105} \\\Leftrightarrow & 315x+54x& = & 5+105 \\\Leftrightarrow & \color{red}{369} x& = & 110 \\\Leftrightarrow & x = \frac{110}{369} & & \\ & V = \left\{ \frac{110}{369} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+12} & = & \color{red}{98x} +63 \\\Leftrightarrow & 140x \color{red}{+12} \color{blue}{-12} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{-12} \\\Leftrightarrow & 140x-98x& = & 63-12 \\\Leftrightarrow & \color{red}{42} x& = & 51 \\\Leftrightarrow & x = \frac{51}{42} & & \\\Leftrightarrow & x = \frac{17}{14} & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 28x+\frac{28}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x+ \frac{224}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{+224} & = & \color{red}{440x} +77 \\\Leftrightarrow & 2464x \color{red}{+224} \color{blue}{-224} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{-224} \\\Leftrightarrow & 2464x-440x& = & 77-224 \\\Leftrightarrow & \color{red}{2024} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{2024} & & \\ & V = \left\{ \frac{-147}{2024} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-100} & = & \color{red}{-245x} +21 \\\Leftrightarrow & 420x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & 420x+245x& = & 21+100 \\\Leftrightarrow & \color{red}{665} x& = & 121 \\\Leftrightarrow & x = \frac{121}{665} & & \\ & V = \left\{ \frac{121}{665} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -4x-\frac{8}{9}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-144}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -144x \color{red}{-32} & = & \color{red}{180x} +15 \\\Leftrightarrow & -144x \color{red}{-32} \color{blue}{+32} \color{blue}{-180x} & = & \color{red}{180x} +15 \color{blue}{-180x} \color{blue}{+32} \\\Leftrightarrow & -144x-180x& = & 15+32 \\\Leftrightarrow & \color{red}{-324} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-324} & & \\\Leftrightarrow & x = \frac{-47}{324} & & \\ & V = \left\{ \frac{-47}{324} \right\} & \\\end{align}\)
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