Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & -3x+\frac{7}{12} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-840}{ \color{blue}{60} }x+ \frac{168}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{-180x} +35 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{+180x} & = & \color{red}{-180x} +35 \color{blue}{+180x} \color{blue}{-168} \\\Leftrightarrow & -840x+180x& = & 35-168 \\\Leftrightarrow & \color{red}{-660} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-660} & & \\\Leftrightarrow & x = \frac{133}{660} & & \\ & V = \left\{ \frac{133}{660} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & 1155x+539x& = & 42+66 \\\Leftrightarrow & \color{red}{1694} x& = & 108 \\\Leftrightarrow & x = \frac{108}{1694} & & \\\Leftrightarrow & x = \frac{54}{847} & & \\ & V = \left\{ \frac{54}{847} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{385x} +45 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +45 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1650x-385x& = & 45-132 \\\Leftrightarrow & \color{red}{1265} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{1265} & & \\ & V = \left\{ \frac{-87}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1260}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1260x \color{red}{-300} & = & \color{red}{-350x} +21 \\\Leftrightarrow & 1260x \color{red}{-300} \color{blue}{+300} \color{blue}{+350x} & = & \color{red}{-350x} +21 \color{blue}{+350x} \color{blue}{+300} \\\Leftrightarrow & 1260x+350x& = & 21+300 \\\Leftrightarrow & \color{red}{1610} x& = & 321 \\\Leftrightarrow & x = \frac{321}{1610} & & \\ & V = \left\{ \frac{321}{1610} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & 792x+165x& = & 44+54 \\\Leftrightarrow & \color{red}{957} x& = & 98 \\\Leftrightarrow & x = \frac{98}{957} & & \\ & V = \left\{ \frac{98}{957} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{105x} +70 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 252x-105x& = & 70-90 \\\Leftrightarrow & \color{red}{147} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{147} & & \\ & V = \left\{ \frac{-20}{147} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-110} & = & \color{red}{385x} +56 \\\Leftrightarrow & 462x \color{red}{-110} \color{blue}{+110} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{+110} \\\Leftrightarrow & 462x-385x& = & 56+110 \\\Leftrightarrow & \color{red}{77} x& = & 166 \\\Leftrightarrow & x = \frac{166}{77} & & \\ & V = \left\{ \frac{166}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 210x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{35} x& = & 134 \\\Leftrightarrow & x = \frac{134}{35} & & \\ & V = \left\{ \frac{134}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{16}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+176} & = & \color{red}{231x} +18 \\\Leftrightarrow & 528x \color{red}{+176} \color{blue}{-176} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{-176} \\\Leftrightarrow & 528x-231x& = & 18-176 \\\Leftrightarrow & \color{red}{297} x& = & -158 \\\Leftrightarrow & x = \frac{-158}{297} & & \\ & V = \left\{ \frac{-158}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{9})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{4}{9}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-28} & = & \color{red}{-441x} +18 \\\Leftrightarrow & 504x \color{red}{-28} \color{blue}{+28} \color{blue}{+441x} & = & \color{red}{-441x} +18 \color{blue}{+441x} \color{blue}{+28} \\\Leftrightarrow & 504x+441x& = & 18+28 \\\Leftrightarrow & \color{red}{945} x& = & 46 \\\Leftrightarrow & x = \frac{46}{945} & & \\ & V = \left\{ \frac{46}{945} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{4})& = & 4x+\frac{5}{2} \\\Leftrightarrow & -25x+\frac{15}{4}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{+15} & = & \color{red}{16x} +10 \\\Leftrightarrow & -100x \color{red}{+15} \color{blue}{-15} \color{blue}{-16x} & = & \color{red}{16x} +10 \color{blue}{-16x} \color{blue}{-15} \\\Leftrightarrow & -100x-16x& = & 10-15 \\\Leftrightarrow & \color{red}{-116} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-116} & & \\\Leftrightarrow & x = \frac{5}{116} & & \\ & V = \left\{ \frac{5}{116} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 18x-\frac{24}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-168} & = & \color{red}{385x} +22 \\\Leftrightarrow & 1386x \color{red}{-168} \color{blue}{+168} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+168} \\\Leftrightarrow & 1386x-385x& = & 22+168 \\\Leftrightarrow & \color{red}{1001} x& = & 190 \\\Leftrightarrow & x = \frac{190}{1001} & & \\ & V = \left\{ \frac{190}{1001} \right\} & \\\end{align}\)
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