Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & -630x+441x& = & 14+90 \\\Leftrightarrow & \color{red}{-189} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-189} & & \\\Leftrightarrow & x = \frac{-104}{189} & & \\ & V = \left\{ \frac{-104}{189} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-126} & = & \color{red}{-539x} +55 \\\Leftrightarrow & -1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & -1848x+539x& = & 55+126 \\\Leftrightarrow & \color{red}{-1309} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1309} & & \\\Leftrightarrow & x = \frac{-181}{1309} & & \\ & V = \left\{ \frac{-181}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & 8x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & 8x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{440x} +35 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{-440x} & = & \color{red}{440x} +35 \color{blue}{-440x} \color{blue}{-66} \\\Leftrightarrow & -825x-440x& = & 35-66 \\\Leftrightarrow & \color{red}{-1265} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1265} & & \\\Leftrightarrow & x = \frac{31}{1265} & & \\ & V = \left\{ \frac{31}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{11})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 20x-\frac{25}{11}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-25} & = & \color{red}{-99x} +8 \\\Leftrightarrow & 220x \color{red}{-25} \color{blue}{+25} \color{blue}{+99x} & = & \color{red}{-99x} +8 \color{blue}{+99x} \color{blue}{+25} \\\Leftrightarrow & 220x+99x& = & 8+25 \\\Leftrightarrow & \color{red}{319} x& = & 33 \\\Leftrightarrow & x = \frac{33}{319} & & \\\Leftrightarrow & x = \frac{3}{29} & & \\ & V = \left\{ \frac{3}{29} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{20}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{140x} +20 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +20 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -252x-140x& = & 20+105 \\\Leftrightarrow & \color{red}{-392} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-392} & & \\\Leftrightarrow & x = \frac{-125}{392} & & \\ & V = \left\{ \frac{-125}{392} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{-66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -693x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -693x+539x& = & 42+66 \\\Leftrightarrow & \color{red}{-154} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-154} & & \\\Leftrightarrow & x = \frac{-54}{77} & & \\ & V = \left\{ \frac{-54}{77} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{-360x} +48 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{+360x} & = & \color{red}{-360x} +48 \color{blue}{+360x} \color{blue}{+105} \\\Leftrightarrow & 560x+360x& = & 48+105 \\\Leftrightarrow & \color{red}{920} x& = & 153 \\\Leftrightarrow & x = \frac{153}{920} & & \\ & V = \left\{ \frac{153}{920} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1200}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1200x \color{red}{+192} & = & \color{red}{280x} +45 \\\Leftrightarrow & -1200x \color{red}{+192} \color{blue}{-192} \color{blue}{-280x} & = & \color{red}{280x} +45 \color{blue}{-280x} \color{blue}{-192} \\\Leftrightarrow & -1200x-280x& = & 45-192 \\\Leftrightarrow & \color{red}{-1480} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{-1480} & & \\\Leftrightarrow & x = \frac{147}{1480} & & \\ & V = \left\{ \frac{147}{1480} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 8x+\frac{7}{2} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{126}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 126x \color{red}{-12} & = & \color{red}{112x} +49 \\\Leftrightarrow & 126x \color{red}{-12} \color{blue}{+12} \color{blue}{-112x} & = & \color{red}{112x} +49 \color{blue}{-112x} \color{blue}{+12} \\\Leftrightarrow & 126x-112x& = & 49+12 \\\Leftrightarrow & \color{red}{14} x& = & 61 \\\Leftrightarrow & x = \frac{61}{14} & & \\ & V = \left\{ \frac{61}{14} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+30} & = & \color{red}{175x} +14 \\\Leftrightarrow & -315x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +14 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & -315x-175x& = & 14-30 \\\Leftrightarrow & \color{red}{-490} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-490} & & \\\Leftrightarrow & x = \frac{8}{245} & & \\ & V = \left\{ \frac{8}{245} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{16}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+16} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -180x \color{red}{+16} \color{blue}{-16} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-16} \\\Leftrightarrow & -180x+63x& = & 6-16 \\\Leftrightarrow & \color{red}{-117} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-117} & & \\\Leftrightarrow & x = \frac{10}{117} & & \\ & V = \left\{ \frac{10}{117} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{8})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 28x+\frac{21}{8}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+63} & = & \color{red}{-120x} +32 \\\Leftrightarrow & 672x \color{red}{+63} \color{blue}{-63} \color{blue}{+120x} & = & \color{red}{-120x} +32 \color{blue}{+120x} \color{blue}{-63} \\\Leftrightarrow & 672x+120x& = & 32-63 \\\Leftrightarrow & \color{red}{792} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{792} & & \\ & V = \left\{ \frac{-31}{792} \right\} & \\\end{align}\)
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