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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & -4x+\frac{7}{8} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{-288}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{-160} & = & \color{red}{-288x} +63 \\\Leftrightarrow & -1080x \color{red}{-160} \color{blue}{+160} \color{blue}{+288x} & = & \color{red}{-288x} +63 \color{blue}{+288x} \color{blue}{+160} \\\Leftrightarrow & -1080x+288x& = & 63+160 \\\Leftrightarrow & \color{red}{-792} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-792} & & \\\Leftrightarrow & x = \frac{-223}{792} & & \\ & V = \left\{ \frac{-223}{792} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{9})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -6x+\frac{10}{9}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+10} & = & \color{red}{63x} +21 \\\Leftrightarrow & -54x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +21 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & -54x-63x& = & 21-10 \\\Leftrightarrow & \color{red}{-117} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-117} & & \\\Leftrightarrow & x = \frac{-11}{117} & & \\ & V = \left\{ \frac{-11}{117} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & -6x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -6x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{-100} & = & \color{red}{-210x} +42 \\\Leftrightarrow & -875x \color{red}{-100} \color{blue}{+100} \color{blue}{+210x} & = & \color{red}{-210x} +42 \color{blue}{+210x} \color{blue}{+100} \\\Leftrightarrow & -875x+210x& = & 42+100 \\\Leftrightarrow & \color{red}{-665} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-665} & & \\\Leftrightarrow & x = \frac{-142}{665} & & \\ & V = \left\{ \frac{-142}{665} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{18}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-198} & = & \color{red}{539x} +56 \\\Leftrightarrow & -2310x \color{red}{-198} \color{blue}{+198} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{+198} \\\Leftrightarrow & -2310x-539x& = & 56+198 \\\Leftrightarrow & \color{red}{-2849} x& = & 254 \\\Leftrightarrow & x = \frac{254}{-2849} & & \\\Leftrightarrow & x = \frac{-254}{2849} & & \\ & V = \left\{ \frac{-254}{2849} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-75} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 825x \color{red}{-75} \color{blue}{+75} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+75} \\\Leftrightarrow & 825x+385x& = & 22+75 \\\Leftrightarrow & \color{red}{1210} x& = & 97 \\\Leftrightarrow & x = \frac{97}{1210} & & \\ & V = \left\{ \frac{97}{1210} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{2})& = & -2x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{7}{2}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{140}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} })& = & (\frac{-8}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 140x \color{red}{+14} & = & \color{red}{-8x} +3 \\\Leftrightarrow & 140x \color{red}{+14} \color{blue}{-14} \color{blue}{+8x} & = & \color{red}{-8x} +3 \color{blue}{+8x} \color{blue}{-14} \\\Leftrightarrow & 140x+8x& = & 3-14 \\\Leftrightarrow & \color{red}{148} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{148} & & \\ & V = \left\{ \frac{-11}{148} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -18x+\frac{30}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+150} & = & \color{red}{-385x} +88 \\\Leftrightarrow & -990x \color{red}{+150} \color{blue}{-150} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-150} \\\Leftrightarrow & -990x+385x& = & 88-150 \\\Leftrightarrow & \color{red}{-605} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-605} & & \\\Leftrightarrow & x = \frac{62}{605} & & \\ & V = \left\{ \frac{62}{605} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{196x} +36 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +36 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & 252x-196x& = & 36+105 \\\Leftrightarrow & \color{red}{56} x& = & 141 \\\Leftrightarrow & x = \frac{141}{56} & & \\ & V = \left\{ \frac{141}{56} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{+162} & = & \color{red}{693x} +44 \\\Leftrightarrow & 2970x \color{red}{+162} \color{blue}{-162} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-162} \\\Leftrightarrow & 2970x-693x& = & 44-162 \\\Leftrightarrow & \color{red}{2277} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{2277} & & \\ & V = \left\{ \frac{-118}{2277} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{10}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{-10} & = & \color{red}{21x} +4 \\\Leftrightarrow & 18x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 18x-21x& = & 4+10 \\\Leftrightarrow & \color{red}{-3} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-3} & & \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+330} & = & \color{red}{-385x} +70 \\\Leftrightarrow & -924x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -924x+385x& = & 70-330 \\\Leftrightarrow & \color{red}{-539} x& = & -260 \\\Leftrightarrow & x = \frac{-260}{-539} & & \\\Leftrightarrow & x = \frac{260}{539} & & \\ & V = \left\{ \frac{260}{539} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+30} & = & \color{red}{55x} +7 \\\Leftrightarrow & -132x \color{red}{+30} \color{blue}{-30} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{-30} \\\Leftrightarrow & -132x-55x& = & 7-30 \\\Leftrightarrow & \color{red}{-187} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-187} & & \\\Leftrightarrow & x = \frac{23}{187} & & \\ & V = \left\{ \frac{23}{187} \right\} & \\\end{align}\)
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