Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{50x} +45 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & -240x-50x& = & 45+48 \\\Leftrightarrow & \color{red}{-290} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-290} & & \\\Leftrightarrow & x = \frac{-93}{290} & & \\ & V = \left\{ \frac{-93}{290} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{9}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{63}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-63} & = & \color{red}{385x} +44 \\\Leftrightarrow & -924x \color{red}{-63} \color{blue}{+63} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+63} \\\Leftrightarrow & -924x-385x& = & 44+63 \\\Leftrightarrow & \color{red}{-1309} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-1309} & & \\\Leftrightarrow & x = \frac{-107}{1309} & & \\ & V = \left\{ \frac{-107}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{-48x} +32 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{+48x} & = & \color{red}{-48x} +32 \color{blue}{+48x} \color{blue}{+45} \\\Leftrightarrow & -180x+48x& = & 32+45 \\\Leftrightarrow & \color{red}{-132} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-132} & & \\\Leftrightarrow & x = \frac{-7}{12} & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 756x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & 756x+315x& = & 56+270 \\\Leftrightarrow & \color{red}{1071} x& = & 326 \\\Leftrightarrow & x = \frac{326}{1071} & & \\ & V = \left\{ \frac{326}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{4})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -28x-\frac{21}{4}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-784}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -784x \color{red}{-147} & = & \color{red}{-252x} +8 \\\Leftrightarrow & -784x \color{red}{-147} \color{blue}{+147} \color{blue}{+252x} & = & \color{red}{-252x} +8 \color{blue}{+252x} \color{blue}{+147} \\\Leftrightarrow & -784x+252x& = & 8+147 \\\Leftrightarrow & \color{red}{-532} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-532} & & \\\Leftrightarrow & x = \frac{-155}{532} & & \\ & V = \left\{ \frac{-155}{532} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-96} & = & \color{red}{440x} +99 \\\Leftrightarrow & -1056x \color{red}{-96} \color{blue}{+96} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{+96} \\\Leftrightarrow & -1056x-440x& = & 99+96 \\\Leftrightarrow & \color{red}{-1496} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-1496} & & \\\Leftrightarrow & x = \frac{-195}{1496} & & \\ & V = \left\{ \frac{-195}{1496} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-66} & = & \color{red}{385x} +15 \\\Leftrightarrow & -330x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -330x-385x& = & 15+66 \\\Leftrightarrow & \color{red}{-715} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-715} & & \\\Leftrightarrow & x = \frac{-81}{715} & & \\ & V = \left\{ \frac{-81}{715} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & -8x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{6}{11}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+12} & = & \color{red}{-176x} +33 \\\Leftrightarrow & 330x \color{red}{+12} \color{blue}{-12} \color{blue}{+176x} & = & \color{red}{-176x} +33 \color{blue}{+176x} \color{blue}{-12} \\\Leftrightarrow & 330x+176x& = & 33-12 \\\Leftrightarrow & \color{red}{506} x& = & 21 \\\Leftrightarrow & x = \frac{21}{506} & & \\ & V = \left\{ \frac{21}{506} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+12} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -56x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & -56x+70x& = & 63-12 \\\Leftrightarrow & \color{red}{14} x& = & 51 \\\Leftrightarrow & x = \frac{51}{14} & & \\ & V = \left\{ \frac{51}{14} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{8})& = & 4x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{25}{8}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{225}{ \color{blue}{72} })& = & (\frac{288}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+225} & = & \color{red}{288x} +16 \\\Leftrightarrow & -1080x \color{red}{+225} \color{blue}{-225} \color{blue}{-288x} & = & \color{red}{288x} +16 \color{blue}{-288x} \color{blue}{-225} \\\Leftrightarrow & -1080x-288x& = & 16-225 \\\Leftrightarrow & \color{red}{-1368} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{-1368} & & \\\Leftrightarrow & x = \frac{11}{72} & & \\ & V = \left\{ \frac{11}{72} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{-96} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 600x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 600x+280x& = & 35+96 \\\Leftrightarrow & \color{red}{880} x& = & 131 \\\Leftrightarrow & x = \frac{131}{880} & & \\ & V = \left\{ \frac{131}{880} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{11})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -35x+\frac{21}{11}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+63} & = & \color{red}{132x} +44 \\\Leftrightarrow & -1155x \color{red}{+63} \color{blue}{-63} \color{blue}{-132x} & = & \color{red}{132x} +44 \color{blue}{-132x} \color{blue}{-63} \\\Leftrightarrow & -1155x-132x& = & 44-63 \\\Leftrightarrow & \color{red}{-1287} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-1287} & & \\\Leftrightarrow & x = \frac{19}{1287} & & \\ & V = \left\{ \frac{19}{1287} \right\} & \\\end{align}\)
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