Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -28x-\frac{14}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-14} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -252x \color{red}{-14} \color{blue}{+14} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+14} \\\Leftrightarrow & -252x+63x& = & 30+14 \\\Leftrightarrow & \color{red}{-189} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-189} & & \\\Leftrightarrow & x = \frac{-44}{189} & & \\ & V = \left\{ \frac{-44}{189} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -4x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-20} & = & \color{red}{-56x} +21 \\\Leftrightarrow & 210x \color{red}{-20} \color{blue}{+20} \color{blue}{+56x} & = & \color{red}{-56x} +21 \color{blue}{+56x} \color{blue}{+20} \\\Leftrightarrow & 210x+56x& = & 21+20 \\\Leftrightarrow & \color{red}{266} x& = & 41 \\\Leftrightarrow & x = \frac{41}{266} & & \\ & V = \left\{ \frac{41}{266} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -18x+\frac{18}{11}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+126} & = & \color{red}{-385x} +55 \\\Leftrightarrow & -1386x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +55 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -1386x+385x& = & 55-126 \\\Leftrightarrow & \color{red}{-1001} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-1001} & & \\\Leftrightarrow & x = \frac{71}{1001} & & \\ & V = \left\{ \frac{71}{1001} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{50}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 50x \color{red}{+4} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 50x \color{red}{+4} \color{blue}{-4} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-4} \\\Leftrightarrow & 50x+35x& = & 6-4 \\\Leftrightarrow & \color{red}{85} x& = & 2 \\\Leftrightarrow & x = \frac{2}{85} & & \\ & V = \left\{ \frac{2}{85} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-18} & = & \color{red}{-25x} +4 \\\Leftrightarrow & -120x \color{red}{-18} \color{blue}{+18} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+18} \\\Leftrightarrow & -120x+25x& = & 4+18 \\\Leftrightarrow & \color{red}{-95} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-95} & & \\\Leftrightarrow & x = \frac{-22}{95} & & \\ & V = \left\{ \frac{-22}{95} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{7})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+10} & = & \color{red}{-28x} +8 \\\Leftrightarrow & -105x \color{red}{+10} \color{blue}{-10} \color{blue}{+28x} & = & \color{red}{-28x} +8 \color{blue}{+28x} \color{blue}{-10} \\\Leftrightarrow & -105x+28x& = & 8-10 \\\Leftrightarrow & \color{red}{-77} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-77} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & -6x+\frac{6}{7} \\\Leftrightarrow & -28x-\frac{35}{3}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-245} & = & \color{red}{-126x} +18 \\\Leftrightarrow & -588x \color{red}{-245} \color{blue}{+245} \color{blue}{+126x} & = & \color{red}{-126x} +18 \color{blue}{+126x} \color{blue}{+245} \\\Leftrightarrow & -588x+126x& = & 18+245 \\\Leftrightarrow & \color{red}{-462} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-462} & & \\\Leftrightarrow & x = \frac{-263}{462} & & \\ & V = \left\{ \frac{-263}{462} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -24x-\frac{24}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-72} & = & \color{red}{231x} +110 \\\Leftrightarrow & -792x \color{red}{-72} \color{blue}{+72} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+72} \\\Leftrightarrow & -792x-231x& = & 110+72 \\\Leftrightarrow & \color{red}{-1023} x& = & 182 \\\Leftrightarrow & x = \frac{182}{-1023} & & \\\Leftrightarrow & x = \frac{-182}{1023} & & \\ & V = \left\{ \frac{-182}{1023} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{175x} +40 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 210x-175x& = & 40-84 \\\Leftrightarrow & \color{red}{35} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{35} & & \\ & V = \left\{ \frac{-44}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+54} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 594x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & 594x+165x& = & 22-54 \\\Leftrightarrow & \color{red}{759} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{759} & & \\ & V = \left\{ \frac{-32}{759} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & 396x+231x& = & 88-54 \\\Leftrightarrow & \color{red}{627} x& = & 34 \\\Leftrightarrow & x = \frac{34}{627} & & \\ & V = \left\{ \frac{34}{627} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{9})& = & 8x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{10}{9}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{+20} & = & \color{red}{144x} +27 \\\Leftrightarrow & -270x \color{red}{+20} \color{blue}{-20} \color{blue}{-144x} & = & \color{red}{144x} +27 \color{blue}{-144x} \color{blue}{-20} \\\Leftrightarrow & -270x-144x& = & 27-20 \\\Leftrightarrow & \color{red}{-414} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-414} & & \\\Leftrightarrow & x = \frac{-7}{414} & & \\ & V = \left\{ \frac{-7}{414} \right\} & \\\end{align}\)