Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{15}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+15} & = & \color{red}{49x} +4 \\\Leftrightarrow & -140x \color{red}{+15} \color{blue}{-15} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{-15} \\\Leftrightarrow & -140x-49x& = & 4-15 \\\Leftrightarrow & \color{red}{-189} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-189} & & \\\Leftrightarrow & x = \frac{11}{189} & & \\ & V = \left\{ \frac{11}{189} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-154} & = & \color{red}{297x} +12 \\\Leftrightarrow & 924x \color{red}{-154} \color{blue}{+154} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{+154} \\\Leftrightarrow & 924x-297x& = & 12+154 \\\Leftrightarrow & \color{red}{627} x& = & 166 \\\Leftrightarrow & x = \frac{166}{627} & & \\ & V = \left\{ \frac{166}{627} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 30x+\frac{12}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{+24} & = & \color{red}{154x} +99 \\\Leftrightarrow & 660x \color{red}{+24} \color{blue}{-24} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-24} \\\Leftrightarrow & 660x-154x& = & 99-24 \\\Leftrightarrow & \color{red}{506} x& = & 75 \\\Leftrightarrow & x = \frac{75}{506} & & \\ & V = \left\{ \frac{75}{506} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{18}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{198}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+198} & = & \color{red}{-385x} +56 \\\Leftrightarrow & 924x \color{red}{+198} \color{blue}{-198} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-198} \\\Leftrightarrow & 924x+385x& = & 56-198 \\\Leftrightarrow & \color{red}{1309} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{1309} & & \\ & V = \left\{ \frac{-142}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{120x} +10 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{+36} \\\Leftrightarrow & -225x-120x& = & 10+36 \\\Leftrightarrow & \color{red}{-345} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-345} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+40} & = & \color{red}{42x} +9 \\\Leftrightarrow & -60x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & -60x-42x& = & 9-40 \\\Leftrightarrow & \color{red}{-102} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-102} & & \\\Leftrightarrow & x = \frac{31}{102} & & \\ & V = \left\{ \frac{31}{102} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & -80x+90x& = & 45+24 \\\Leftrightarrow & \color{red}{10} x& = & 69 \\\Leftrightarrow & x = \frac{69}{10} & & \\ & V = \left\{ \frac{69}{10} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{9})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{-385} & = & \color{red}{297x} +18 \\\Leftrightarrow & -1386x \color{red}{-385} \color{blue}{+385} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+385} \\\Leftrightarrow & -1386x-297x& = & 18+385 \\\Leftrightarrow & \color{red}{-1683} x& = & 403 \\\Leftrightarrow & x = \frac{403}{-1683} & & \\\Leftrightarrow & x = \frac{-403}{1683} & & \\ & V = \left\{ \frac{-403}{1683} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -25x-\frac{25}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{275}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-275} & = & \color{red}{231x} +30 \\\Leftrightarrow & -825x \color{red}{-275} \color{blue}{+275} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{+275} \\\Leftrightarrow & -825x-231x& = & 30+275 \\\Leftrightarrow & \color{red}{-1056} x& = & 305 \\\Leftrightarrow & x = \frac{305}{-1056} & & \\\Leftrightarrow & x = \frac{-305}{1056} & & \\ & V = \left\{ \frac{-305}{1056} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & 2x+\frac{2}{5} \\\Leftrightarrow & 15x+\frac{6}{11}& = & 2x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+30} & = & \color{red}{110x} +22 \\\Leftrightarrow & 825x \color{red}{+30} \color{blue}{-30} \color{blue}{-110x} & = & \color{red}{110x} +22 \color{blue}{-110x} \color{blue}{-30} \\\Leftrightarrow & 825x-110x& = & 22-30 \\\Leftrightarrow & \color{red}{715} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{715} & & \\ & V = \left\{ \frac{-8}{715} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{5})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{9}{5}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-99} & = & \color{red}{-275x} +40 \\\Leftrightarrow & -660x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +40 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & -660x+275x& = & 40+99 \\\Leftrightarrow & \color{red}{-385} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-385} & & \\\Leftrightarrow & x = \frac{-139}{385} & & \\ & V = \left\{ \frac{-139}{385} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{2})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x- \frac{135}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{-135} & = & \color{red}{144x} +8 \\\Leftrightarrow & -270x \color{red}{-135} \color{blue}{+135} \color{blue}{-144x} & = & \color{red}{144x} +8 \color{blue}{-144x} \color{blue}{+135} \\\Leftrightarrow & -270x-144x& = & 8+135 \\\Leftrightarrow & \color{red}{-414} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-414} & & \\\Leftrightarrow & x = \frac{-143}{414} & & \\ & V = \left\{ \frac{-143}{414} \right\} & \\\end{align}\)
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