Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-48} & = & \color{red}{70x} +45 \\\Leftrightarrow & 300x \color{red}{-48} \color{blue}{+48} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+48} \\\Leftrightarrow & 300x-70x& = & 45+48 \\\Leftrightarrow & \color{red}{230} x& = & 93 \\\Leftrightarrow & x = \frac{93}{230} & & \\ & V = \left\{ \frac{93}{230} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{9})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{-810}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{-80} & = & \color{red}{-810x} +81 \\\Leftrightarrow & -720x \color{red}{-80} \color{blue}{+80} \color{blue}{+810x} & = & \color{red}{-810x} +81 \color{blue}{+810x} \color{blue}{+80} \\\Leftrightarrow & -720x+810x& = & 81+80 \\\Leftrightarrow & \color{red}{90} x& = & 161 \\\Leftrightarrow & x = \frac{161}{90} & & \\ & V = \left\{ \frac{161}{90} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-42} & = & \color{red}{280x} +50 \\\Leftrightarrow & -525x \color{red}{-42} \color{blue}{+42} \color{blue}{-280x} & = & \color{red}{280x} +50 \color{blue}{-280x} \color{blue}{+42} \\\Leftrightarrow & -525x-280x& = & 50+42 \\\Leftrightarrow & \color{red}{-805} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-805} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{270x} +81 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{-270x} & = & \color{red}{270x} +81 \color{blue}{-270x} \color{blue}{-80} \\\Leftrightarrow & -720x-270x& = & 81-80 \\\Leftrightarrow & \color{red}{-990} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-990} & & \\\Leftrightarrow & x = \frac{-1}{990} & & \\ & V = \left\{ \frac{-1}{990} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-100} & = & \color{red}{-175x} +28 \\\Leftrightarrow & -420x \color{red}{-100} \color{blue}{+100} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{+100} \\\Leftrightarrow & -420x+175x& = & 28+100 \\\Leftrightarrow & \color{red}{-245} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-245} & & \\\Leftrightarrow & x = \frac{-128}{245} & & \\ & V = \left\{ \frac{-128}{245} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{54x} +21 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-54x} & = & \color{red}{54x} +21 \color{blue}{-54x} \color{blue}{-40} \\\Leftrightarrow & 120x-54x& = & 21-40 \\\Leftrightarrow & \color{red}{66} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{66} & & \\ & V = \left\{ \frac{-19}{66} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{11})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{15}{11}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+15} & = & \color{red}{33x} +10 \\\Leftrightarrow & 220x \color{red}{+15} \color{blue}{-15} \color{blue}{-33x} & = & \color{red}{33x} +10 \color{blue}{-33x} \color{blue}{-15} \\\Leftrightarrow & 220x-33x& = & 10-15 \\\Leftrightarrow & \color{red}{187} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{187} & & \\ & V = \left\{ \frac{-5}{187} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{11})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 24x+\frac{30}{11}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+210} & = & \color{red}{-385x} +99 \\\Leftrightarrow & 1848x \color{red}{+210} \color{blue}{-210} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{-210} \\\Leftrightarrow & 1848x+385x& = & 99-210 \\\Leftrightarrow & \color{red}{2233} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{2233} & & \\ & V = \left\{ \frac{-111}{2233} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-140} & = & \color{red}{147x} +18 \\\Leftrightarrow & -210x \color{red}{-140} \color{blue}{+140} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{+140} \\\Leftrightarrow & -210x-147x& = & 18+140 \\\Leftrightarrow & \color{red}{-357} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-357} & & \\\Leftrightarrow & x = \frac{-158}{357} & & \\ & V = \left\{ \frac{-158}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{11})& = & -3x+\frac{7}{11} \\\Leftrightarrow & -8x-\frac{8}{11}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-8} & = & \color{red}{-33x} +7 \\\Leftrightarrow & -88x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +7 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & -88x+33x& = & 7+8 \\\Leftrightarrow & \color{red}{-55} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-55} & & \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-168} & = & \color{red}{245x} +50 \\\Leftrightarrow & 1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & 1050x-245x& = & 50+168 \\\Leftrightarrow & \color{red}{805} x& = & 218 \\\Leftrightarrow & x = \frac{218}{805} & & \\ & V = \left\{ \frac{218}{805} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+63} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 462x \color{red}{+63} \color{blue}{-63} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{-63} \\\Leftrightarrow & 462x+297x& = & 22-63 \\\Leftrightarrow & \color{red}{759} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{759} & & \\ & V = \left\{ \frac{-41}{759} \right\} & \\\end{align}\)
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