Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{6}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{-50x} +3 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{+12} \\\Leftrightarrow & -120x+50x& = & 3+12 \\\Leftrightarrow & \color{red}{-70} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-70} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{-48} & = & \color{red}{-504x} +49 \\\Leftrightarrow & -448x \color{red}{-48} \color{blue}{+48} \color{blue}{+504x} & = & \color{red}{-504x} +49 \color{blue}{+504x} \color{blue}{+48} \\\Leftrightarrow & -448x+504x& = & 49+48 \\\Leftrightarrow & \color{red}{56} x& = & 97 \\\Leftrightarrow & x = \frac{97}{56} & & \\ & V = \left\{ \frac{97}{56} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{-48} & = & \color{red}{140x} +25 \\\Leftrightarrow & -320x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +25 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & -320x-140x& = & 25+48 \\\Leftrightarrow & \color{red}{-460} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-460} & & \\\Leftrightarrow & x = \frac{-73}{460} & & \\ & V = \left\{ \frac{-73}{460} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -25x+\frac{10}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+10} & = & \color{red}{63x} +30 \\\Leftrightarrow & -225x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & -225x-63x& = & 30-10 \\\Leftrightarrow & \color{red}{-288} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-288} & & \\\Leftrightarrow & x = \frac{-5}{72} & & \\ & V = \left\{ \frac{-5}{72} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{28}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-28} & = & \color{red}{-9x} +10 \\\Leftrightarrow & -105x \color{red}{-28} \color{blue}{+28} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+28} \\\Leftrightarrow & -105x+9x& = & 10+28 \\\Leftrightarrow & \color{red}{-96} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-96} & & \\\Leftrightarrow & x = \frac{-19}{48} & & \\ & V = \left\{ \frac{-19}{48} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{+12} & = & \color{red}{15x} +2 \\\Leftrightarrow & -100x \color{red}{+12} \color{blue}{-12} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{-12} \\\Leftrightarrow & -100x-15x& = & 2-12 \\\Leftrightarrow & \color{red}{-115} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-115} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+16} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -120x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & -120x+42x& = & 5-16 \\\Leftrightarrow & \color{red}{-78} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-78} & & \\\Leftrightarrow & x = \frac{11}{78} & & \\ & V = \left\{ \frac{11}{78} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{5})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{14}{5}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-42} & = & \color{red}{-30x} +10 \\\Leftrightarrow & 525x \color{red}{-42} \color{blue}{+42} \color{blue}{+30x} & = & \color{red}{-30x} +10 \color{blue}{+30x} \color{blue}{+42} \\\Leftrightarrow & 525x+30x& = & 10+42 \\\Leftrightarrow & \color{red}{555} x& = & 52 \\\Leftrightarrow & x = \frac{52}{555} & & \\ & V = \left\{ \frac{52}{555} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-40} & = & \color{red}{252x} +21 \\\Leftrightarrow & -560x \color{red}{-40} \color{blue}{+40} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{+40} \\\Leftrightarrow & -560x-252x& = & 21+40 \\\Leftrightarrow & \color{red}{-812} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-812} & & \\\Leftrightarrow & x = \frac{-61}{812} & & \\ & V = \left\{ \frac{-61}{812} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{4}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+8} & = & \color{red}{110x} +99 \\\Leftrightarrow & 176x \color{red}{+8} \color{blue}{-8} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-8} \\\Leftrightarrow & 176x-110x& = & 99-8 \\\Leftrightarrow & \color{red}{66} x& = & 91 \\\Leftrightarrow & x = \frac{91}{66} & & \\ & V = \left\{ \frac{91}{66} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+48} & = & \color{red}{100x} +35 \\\Leftrightarrow & 240x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & 240x-100x& = & 35-48 \\\Leftrightarrow & \color{red}{140} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{140} & & \\ & V = \left\{ \frac{-13}{140} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{7})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -35x+4& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{36}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+36} & = & \color{red}{81x} +8 \\\Leftrightarrow & -315x \color{red}{+36} \color{blue}{-36} \color{blue}{-81x} & = & \color{red}{81x} +8 \color{blue}{-81x} \color{blue}{-36} \\\Leftrightarrow & -315x-81x& = & 8-36 \\\Leftrightarrow & \color{red}{-396} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-396} & & \\\Leftrightarrow & x = \frac{7}{99} & & \\ & V = \left\{ \frac{7}{99} \right\} & \\\end{align}\)
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