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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{3}{5} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-12} & = & \color{red}{-20x} +3 \\\Leftrightarrow & -75x \color{red}{-12} \color{blue}{+12} \color{blue}{+20x} & = & \color{red}{-20x} +3 \color{blue}{+20x} \color{blue}{+12} \\\Leftrightarrow & -75x+20x& = & 3+12 \\\Leftrightarrow & \color{red}{-55} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-55} & & \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{77x} +2 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{+30} \\\Leftrightarrow & -330x-77x& = & 2+30 \\\Leftrightarrow & \color{red}{-407} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-407} & & \\\Leftrightarrow & x = \frac{-32}{407} & & \\ & V = \left\{ \frac{-32}{407} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{9})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{16}{9}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{32}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+32} & = & \color{red}{126x} +27 \\\Leftrightarrow & 144x \color{red}{+32} \color{blue}{-32} \color{blue}{-126x} & = & \color{red}{126x} +27 \color{blue}{-126x} \color{blue}{-32} \\\Leftrightarrow & 144x-126x& = & 27-32 \\\Leftrightarrow & \color{red}{18} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{18} & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{-48} & = & \color{red}{-140x} +25 \\\Leftrightarrow & -320x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +25 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -320x+140x& = & 25+48 \\\Leftrightarrow & \color{red}{-180} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-180} & & \\\Leftrightarrow & x = \frac{-73}{180} & & \\ & V = \left\{ \frac{-73}{180} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{7})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+100} & = & \color{red}{-175x} +49 \\\Leftrightarrow & -420x \color{red}{+100} \color{blue}{-100} \color{blue}{+175x} & = & \color{red}{-175x} +49 \color{blue}{+175x} \color{blue}{-100} \\\Leftrightarrow & -420x+175x& = & 49-100 \\\Leftrightarrow & \color{red}{-245} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-245} & & \\\Leftrightarrow & x = \frac{51}{245} & & \\ & V = \left\{ \frac{51}{245} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{12}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-36} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{-36} \color{blue}{+36} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+36} \\\Leftrightarrow & -126x-147x& = & 56+36 \\\Leftrightarrow & \color{red}{-273} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-273} & & \\\Leftrightarrow & x = \frac{-92}{273} & & \\ & V = \left\{ \frac{-92}{273} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{2})& = & -8x+\frac{4}{7} \\\Leftrightarrow & 35x+\frac{7}{2}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{490}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 490x \color{red}{+49} & = & \color{red}{-112x} +8 \\\Leftrightarrow & 490x \color{red}{+49} \color{blue}{-49} \color{blue}{+112x} & = & \color{red}{-112x} +8 \color{blue}{+112x} \color{blue}{-49} \\\Leftrightarrow & 490x+112x& = & 8-49 \\\Leftrightarrow & \color{red}{602} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{602} & & \\ & V = \left\{ \frac{-41}{602} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{297x} +18 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & -1155x-297x& = & 18-154 \\\Leftrightarrow & \color{red}{-1452} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-1452} & & \\\Leftrightarrow & x = \frac{34}{363} & & \\ & V = \left\{ \frac{34}{363} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+264} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 660x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 660x+275x& = & 50-264 \\\Leftrightarrow & \color{red}{935} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{935} & & \\ & V = \left\{ \frac{-214}{935} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+330} & = & \color{red}{-385x} +56 \\\Leftrightarrow & 1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & 1848x+385x& = & 56-330 \\\Leftrightarrow & \color{red}{2233} x& = & -274 \\\Leftrightarrow & x = \frac{-274}{2233} & & \\ & V = \left\{ \frac{-274}{2233} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & 330x+231x& = & 22+30 \\\Leftrightarrow & \color{red}{561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{561} & & \\ & V = \left\{ \frac{52}{561} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{15}{8}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-528}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -528x \color{red}{-165} & = & \color{red}{-616x} +80 \\\Leftrightarrow & -528x \color{red}{-165} \color{blue}{+165} \color{blue}{+616x} & = & \color{red}{-616x} +80 \color{blue}{+616x} \color{blue}{+165} \\\Leftrightarrow & -528x+616x& = & 80+165 \\\Leftrightarrow & \color{red}{88} x& = & 245 \\\Leftrightarrow & x = \frac{245}{88} & & \\ & V = \left\{ \frac{245}{88} \right\} & \\\end{align}\)
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