Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 126x+105x& = & 70-18 \\\Leftrightarrow & \color{red}{231} x& = & 52 \\\Leftrightarrow & x = \frac{52}{231} & & \\ & V = \left\{ \frac{52}{231} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{140x} +16 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 300x-140x& = & 16+75 \\\Leftrightarrow & \color{red}{160} x& = & 91 \\\Leftrightarrow & x = \frac{91}{160} & & \\ & V = \left\{ \frac{91}{160} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & -8x+\frac{9}{8} \\\Leftrightarrow & 21x-\frac{35}{9}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1512}{ \color{blue}{72} }x- \frac{280}{ \color{blue}{72} })& = & (\frac{-576}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1512x \color{red}{-280} & = & \color{red}{-576x} +81 \\\Leftrightarrow & 1512x \color{red}{-280} \color{blue}{+280} \color{blue}{+576x} & = & \color{red}{-576x} +81 \color{blue}{+576x} \color{blue}{+280} \\\Leftrightarrow & 1512x+576x& = & 81+280 \\\Leftrightarrow & \color{red}{2088} x& = & 361 \\\Leftrightarrow & x = \frac{361}{2088} & & \\ & V = \left\{ \frac{361}{2088} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1080}{ \color{blue}{60} }x+ \frac{288}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1080x \color{red}{+288} & = & \color{red}{-300x} +35 \\\Leftrightarrow & 1080x \color{red}{+288} \color{blue}{-288} \color{blue}{+300x} & = & \color{red}{-300x} +35 \color{blue}{+300x} \color{blue}{-288} \\\Leftrightarrow & 1080x+300x& = & 35-288 \\\Leftrightarrow & \color{red}{1380} x& = & -253 \\\Leftrightarrow & x = \frac{-253}{1380} & & \\\Leftrightarrow & x = \frac{-11}{60} & & \\ & V = \left\{ \frac{-11}{60} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{-147} & = & \color{red}{-112x} +80 \\\Leftrightarrow & 1960x \color{red}{-147} \color{blue}{+147} \color{blue}{+112x} & = & \color{red}{-112x} +80 \color{blue}{+112x} \color{blue}{+147} \\\Leftrightarrow & 1960x+112x& = & 80+147 \\\Leftrightarrow & \color{red}{2072} x& = & 227 \\\Leftrightarrow & x = \frac{227}{2072} & & \\ & V = \left\{ \frac{227}{2072} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{11})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-80} & = & \color{red}{-495x} +66 \\\Leftrightarrow & -440x \color{red}{-80} \color{blue}{+80} \color{blue}{+495x} & = & \color{red}{-495x} +66 \color{blue}{+495x} \color{blue}{+80} \\\Leftrightarrow & -440x+495x& = & 66+80 \\\Leftrightarrow & \color{red}{55} x& = & 146 \\\Leftrightarrow & x = \frac{146}{55} & & \\ & V = \left\{ \frac{146}{55} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & 4x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{220x} +35 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{-220x} & = & \color{red}{220x} +35 \color{blue}{-220x} \color{blue}{-132} \\\Leftrightarrow & -825x-220x& = & 35-132 \\\Leftrightarrow & \color{red}{-1045} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1045} & & \\\Leftrightarrow & x = \frac{97}{1045} & & \\ & V = \left\{ \frac{97}{1045} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{54x} +9 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-16} \\\Leftrightarrow & -48x-54x& = & 9-16 \\\Leftrightarrow & \color{red}{-102} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-102} & & \\\Leftrightarrow & x = \frac{7}{102} & & \\ & V = \left\{ \frac{7}{102} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1440}{ \color{blue}{60} }x+ \frac{288}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1440x \color{red}{+288} & = & \color{red}{-300x} +35 \\\Leftrightarrow & 1440x \color{red}{+288} \color{blue}{-288} \color{blue}{+300x} & = & \color{red}{-300x} +35 \color{blue}{+300x} \color{blue}{-288} \\\Leftrightarrow & 1440x+300x& = & 35-288 \\\Leftrightarrow & \color{red}{1740} x& = & -253 \\\Leftrightarrow & x = \frac{-253}{1740} & & \\ & V = \left\{ \frac{-253}{1740} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{9})& = & 6x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{10}{9}& = & 6x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{+110} & = & \color{red}{594x} +18 \\\Leftrightarrow & 2475x \color{red}{+110} \color{blue}{-110} \color{blue}{-594x} & = & \color{red}{594x} +18 \color{blue}{-594x} \color{blue}{-110} \\\Leftrightarrow & 2475x-594x& = & 18-110 \\\Leftrightarrow & \color{red}{1881} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{1881} & & \\ & V = \left\{ \frac{-92}{1881} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{12}{11}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{-24} & = & \color{red}{-154x} +55 \\\Leftrightarrow & -132x \color{red}{-24} \color{blue}{+24} \color{blue}{+154x} & = & \color{red}{-154x} +55 \color{blue}{+154x} \color{blue}{+24} \\\Leftrightarrow & -132x+154x& = & 55+24 \\\Leftrightarrow & \color{red}{22} x& = & 79 \\\Leftrightarrow & x = \frac{79}{22} & & \\ & V = \left\{ \frac{79}{22} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & -2x+\frac{4}{7} \\\Leftrightarrow & 25x-\frac{15}{7}& = & -2x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-15} & = & \color{red}{-14x} +4 \\\Leftrightarrow & 175x \color{red}{-15} \color{blue}{+15} \color{blue}{+14x} & = & \color{red}{-14x} +4 \color{blue}{+14x} \color{blue}{+15} \\\Leftrightarrow & 175x+14x& = & 4+15 \\\Leftrightarrow & \color{red}{189} x& = & 19 \\\Leftrightarrow & x = \frac{19}{189} & & \\ & V = \left\{ \frac{19}{189} \right\} & \\\end{align}\)
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