Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{27x} +6 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{-27x} & = & \color{red}{27x} +6 \color{blue}{-27x} \color{blue}{+8} \\\Leftrightarrow & -72x-27x& = & 6+8 \\\Leftrightarrow & \color{red}{-99} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-99} & & \\\Leftrightarrow & x = \frac{-14}{99} & & \\ & V = \left\{ \frac{-14}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-63} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -210x \color{red}{-63} \color{blue}{+63} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{+63} \\\Leftrightarrow & -210x+245x& = & 10+63 \\\Leftrightarrow & \color{red}{35} x& = & 73 \\\Leftrightarrow & x = \frac{73}{35} & & \\ & V = \left\{ \frac{73}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{9}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+9} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -45x \color{red}{+9} \color{blue}{-9} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-9} \\\Leftrightarrow & -45x+25x& = & 6-9 \\\Leftrightarrow & \color{red}{-20} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-20} & & \\\Leftrightarrow & x = \frac{3}{20} & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{105x} +45 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 280x-105x& = & 45-84 \\\Leftrightarrow & \color{red}{175} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{175} & & \\ & V = \left\{ \frac{-39}{175} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & -3x+\frac{5}{12} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-672}{ \color{blue}{84} }x+ \frac{240}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -672x \color{red}{+240} & = & \color{red}{-252x} +35 \\\Leftrightarrow & -672x \color{red}{+240} \color{blue}{-240} \color{blue}{+252x} & = & \color{red}{-252x} +35 \color{blue}{+252x} \color{blue}{-240} \\\Leftrightarrow & -672x+252x& = & 35-240 \\\Leftrightarrow & \color{red}{-420} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-420} & & \\\Leftrightarrow & x = \frac{41}{84} & & \\ & V = \left\{ \frac{41}{84} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1568x \color{red}{+147} & = & \color{red}{224x} +80 \\\Leftrightarrow & -1568x \color{red}{+147} \color{blue}{-147} \color{blue}{-224x} & = & \color{red}{224x} +80 \color{blue}{-224x} \color{blue}{-147} \\\Leftrightarrow & -1568x-224x& = & 80-147 \\\Leftrightarrow & \color{red}{-1792} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1792} & & \\\Leftrightarrow & x = \frac{67}{1792} & & \\ & V = \left\{ \frac{67}{1792} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{9})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -8x-\frac{16}{9}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{16}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{27x} +8 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{+16} \\\Leftrightarrow & -72x-27x& = & 8+16 \\\Leftrightarrow & \color{red}{-99} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-99} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{8})& = & -4x+\frac{4}{7} \\\Leftrightarrow & 15x-\frac{25}{8}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{-175} & = & \color{red}{-224x} +32 \\\Leftrightarrow & 840x \color{red}{-175} \color{blue}{+175} \color{blue}{+224x} & = & \color{red}{-224x} +32 \color{blue}{+224x} \color{blue}{+175} \\\Leftrightarrow & 840x+224x& = & 32+175 \\\Leftrightarrow & \color{red}{1064} x& = & 207 \\\Leftrightarrow & x = \frac{207}{1064} & & \\ & V = \left\{ \frac{207}{1064} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{11})& = & -8x+\frac{5}{2} \\\Leftrightarrow & 35x-\frac{14}{11}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{770}{ \color{blue}{22} }x- \frac{28}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 770x \color{red}{-28} & = & \color{red}{-176x} +55 \\\Leftrightarrow & 770x \color{red}{-28} \color{blue}{+28} \color{blue}{+176x} & = & \color{red}{-176x} +55 \color{blue}{+176x} \color{blue}{+28} \\\Leftrightarrow & 770x+176x& = & 55+28 \\\Leftrightarrow & \color{red}{946} x& = & 83 \\\Leftrightarrow & x = \frac{83}{946} & & \\ & V = \left\{ \frac{83}{946} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{4}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{-4} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+4} \\\Leftrightarrow & -20x+45x& = & 6+4 \\\Leftrightarrow & \color{red}{25} x& = & 10 \\\Leftrightarrow & x = \frac{10}{25} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+2)& = & 2x+\frac{6}{5} \\\Leftrightarrow & 21x-14& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{105}{ \color{blue}{5} }x- \frac{70}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 105x \color{red}{-70} & = & \color{red}{10x} +6 \\\Leftrightarrow & 105x \color{red}{-70} \color{blue}{+70} \color{blue}{-10x} & = & \color{red}{10x} +6 \color{blue}{-10x} \color{blue}{+70} \\\Leftrightarrow & 105x-10x& = & 6+70 \\\Leftrightarrow & \color{red}{95} x& = & 76 \\\Leftrightarrow & x = \frac{76}{95} & & \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -80x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{-115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-115} & & \\\Leftrightarrow & x = \frac{-18}{115} & & \\ & V = \left\{ \frac{-18}{115} \right\} & \\\end{align}\)