Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{8})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 14x-\frac{21}{8}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{-147} & = & \color{red}{168x} +16 \\\Leftrightarrow & 784x \color{red}{-147} \color{blue}{+147} \color{blue}{-168x} & = & \color{red}{168x} +16 \color{blue}{-168x} \color{blue}{+147} \\\Leftrightarrow & 784x-168x& = & 16+147 \\\Leftrightarrow & \color{red}{616} x& = & 163 \\\Leftrightarrow & x = \frac{163}{616} & & \\ & V = \left\{ \frac{163}{616} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+330} & = & \color{red}{-385x} +28 \\\Leftrightarrow & 924x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & 924x+385x& = & 28-330 \\\Leftrightarrow & \color{red}{1309} x& = & -302 \\\Leftrightarrow & x = \frac{-302}{1309} & & \\ & V = \left\{ \frac{-302}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-84} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 1540x \color{red}{-84} \color{blue}{+84} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+84} \\\Leftrightarrow & 1540x+539x& = & 110+84 \\\Leftrightarrow & \color{red}{2079} x& = & 194 \\\Leftrightarrow & x = \frac{194}{2079} & & \\ & V = \left\{ \frac{194}{2079} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{-54} & = & \color{red}{-189x} +28 \\\Leftrightarrow & 252x \color{red}{-54} \color{blue}{+54} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+54} \\\Leftrightarrow & 252x+189x& = & 28+54 \\\Leftrightarrow & \color{red}{441} x& = & 82 \\\Leftrightarrow & x = \frac{82}{441} & & \\ & V = \left\{ \frac{82}{441} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -1100x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -1100x+385x& = & 30-132 \\\Leftrightarrow & \color{red}{-715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-715} & & \\\Leftrightarrow & x = \frac{102}{715} & & \\ & V = \left\{ \frac{102}{715} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{11})& = & -2x+\frac{9}{2} \\\Leftrightarrow & -28x-\frac{14}{11}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{28}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-28} & = & \color{red}{-44x} +99 \\\Leftrightarrow & -616x \color{red}{-28} \color{blue}{+28} \color{blue}{+44x} & = & \color{red}{-44x} +99 \color{blue}{+44x} \color{blue}{+28} \\\Leftrightarrow & -616x+44x& = & 99+28 \\\Leftrightarrow & \color{red}{-572} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-572} & & \\\Leftrightarrow & x = \frac{-127}{572} & & \\ & V = \left\{ \frac{-127}{572} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{63x} +56 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 84x-63x& = & 56-30 \\\Leftrightarrow & \color{red}{21} x& = & 26 \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{-35x} +5 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +5 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & 168x+35x& = & 5-30 \\\Leftrightarrow & \color{red}{203} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{203} & & \\ & V = \left\{ \frac{-25}{203} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{175x} +25 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 630x-175x& = & 25-84 \\\Leftrightarrow & \color{red}{455} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{455} & & \\ & V = \left\{ \frac{-59}{455} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 30x-\frac{30}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3300}{ \color{blue}{110} }x- \frac{300}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3300x \color{red}{-300} & = & \color{red}{770x} +77 \\\Leftrightarrow & 3300x \color{red}{-300} \color{blue}{+300} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{+300} \\\Leftrightarrow & 3300x-770x& = & 77+300 \\\Leftrightarrow & \color{red}{2530} x& = & 377 \\\Leftrightarrow & x = \frac{377}{2530} & & \\ & V = \left\{ \frac{377}{2530} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{-165x} +50 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{-132} \\\Leftrightarrow & 880x+165x& = & 50-132 \\\Leftrightarrow & \color{red}{1045} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{1045} & & \\ & V = \left\{ \frac{-82}{1045} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -8x+\frac{5}{3} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -8x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+18} & = & \color{red}{-120x} +25 \\\Leftrightarrow & -225x \color{red}{+18} \color{blue}{-18} \color{blue}{+120x} & = & \color{red}{-120x} +25 \color{blue}{+120x} \color{blue}{-18} \\\Leftrightarrow & -225x+120x& = & 25-18 \\\Leftrightarrow & \color{red}{-105} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-105} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
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