Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{7})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{-160} & = & \color{red}{168x} +21 \\\Leftrightarrow & -448x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & -448x-168x& = & 21+160 \\\Leftrightarrow & \color{red}{-616} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-616} & & \\\Leftrightarrow & x = \frac{-181}{616} & & \\ & V = \left\{ \frac{-181}{616} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{11})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{8}{11}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-24} & = & \color{red}{99x} +22 \\\Leftrightarrow & 264x \color{red}{-24} \color{blue}{+24} \color{blue}{-99x} & = & \color{red}{99x} +22 \color{blue}{-99x} \color{blue}{+24} \\\Leftrightarrow & 264x-99x& = & 22+24 \\\Leftrightarrow & \color{red}{165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{165} & & \\ & V = \left\{ \frac{46}{165} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-88} & = & \color{red}{891x} +54 \\\Leftrightarrow & -792x \color{red}{-88} \color{blue}{+88} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{+88} \\\Leftrightarrow & -792x-891x& = & 54+88 \\\Leftrightarrow & \color{red}{-1683} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-1683} & & \\\Leftrightarrow & x = \frac{-142}{1683} & & \\ & V = \left\{ \frac{-142}{1683} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{275x} +66 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+120} \\\Leftrightarrow & 1320x-275x& = & 66+120 \\\Leftrightarrow & \color{red}{1045} x& = & 186 \\\Leftrightarrow & x = \frac{186}{1045} & & \\ & V = \left\{ \frac{186}{1045} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{11})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 16x-\frac{16}{11}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1408}{ \color{blue}{88} }x- \frac{128}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1408x \color{red}{-128} & = & \color{red}{264x} +99 \\\Leftrightarrow & 1408x \color{red}{-128} \color{blue}{+128} \color{blue}{-264x} & = & \color{red}{264x} +99 \color{blue}{-264x} \color{blue}{+128} \\\Leftrightarrow & 1408x-264x& = & 99+128 \\\Leftrightarrow & \color{red}{1144} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1144} & & \\ & V = \left\{ \frac{227}{1144} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{1}{2})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 14x-\frac{7}{2}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{28}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-28} & = & \color{red}{24x} +7 \\\Leftrightarrow & 112x \color{red}{-28} \color{blue}{+28} \color{blue}{-24x} & = & \color{red}{24x} +7 \color{blue}{-24x} \color{blue}{+28} \\\Leftrightarrow & 112x-24x& = & 7+28 \\\Leftrightarrow & \color{red}{88} x& = & 35 \\\Leftrightarrow & x = \frac{35}{88} & & \\ & V = \left\{ \frac{35}{88} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-180} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1320x \color{red}{-180} \color{blue}{+180} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{+180} \\\Leftrightarrow & 1320x-550x& = & 99+180 \\\Leftrightarrow & \color{red}{770} x& = & 279 \\\Leftrightarrow & x = \frac{279}{770} & & \\ & V = \left\{ \frac{279}{770} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & 6x+\frac{4}{9} \\\Leftrightarrow & -25x-\frac{10}{3}& = & 6x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{-30} & = & \color{red}{54x} +4 \\\Leftrightarrow & -225x \color{red}{-30} \color{blue}{+30} \color{blue}{-54x} & = & \color{red}{54x} +4 \color{blue}{-54x} \color{blue}{+30} \\\Leftrightarrow & -225x-54x& = & 4+30 \\\Leftrightarrow & \color{red}{-279} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-279} & & \\\Leftrightarrow & x = \frac{-34}{279} & & \\ & V = \left\{ \frac{-34}{279} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{16}{3}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+176} & = & \color{red}{165x} +12 \\\Leftrightarrow & 528x \color{red}{+176} \color{blue}{-176} \color{blue}{-165x} & = & \color{red}{165x} +12 \color{blue}{-165x} \color{blue}{-176} \\\Leftrightarrow & 528x-165x& = & 12-176 \\\Leftrightarrow & \color{red}{363} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{363} & & \\ & V = \left\{ \frac{-164}{363} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-48} & = & \color{red}{147x} +14 \\\Leftrightarrow & 420x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & 420x-147x& = & 14+48 \\\Leftrightarrow & \color{red}{273} x& = & 62 \\\Leftrightarrow & x = \frac{62}{273} & & \\ & V = \left\{ \frac{62}{273} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -25x+\frac{15}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+105} & = & \color{red}{385x} +110 \\\Leftrightarrow & -1925x \color{red}{+105} \color{blue}{-105} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-105} \\\Leftrightarrow & -1925x-385x& = & 110-105 \\\Leftrightarrow & \color{red}{-2310} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-2310} & & \\\Leftrightarrow & x = \frac{-1}{462} & & \\ & V = \left\{ \frac{-1}{462} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{9})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{20}{9}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{36}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+20} & = & \color{red}{36x} +24 \\\Leftrightarrow & -225x \color{red}{+20} \color{blue}{-20} \color{blue}{-36x} & = & \color{red}{36x} +24 \color{blue}{-36x} \color{blue}{-20} \\\Leftrightarrow & -225x-36x& = & 24-20 \\\Leftrightarrow & \color{red}{-261} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-261} & & \\\Leftrightarrow & x = \frac{-4}{261} & & \\ & V = \left\{ \frac{-4}{261} \right\} & \\\end{align}\)
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