Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-12} & = & \color{red}{-40x} +6 \\\Leftrightarrow & -75x \color{red}{-12} \color{blue}{+12} \color{blue}{+40x} & = & \color{red}{-40x} +6 \color{blue}{+40x} \color{blue}{+12} \\\Leftrightarrow & -75x+40x& = & 6+12 \\\Leftrightarrow & \color{red}{-35} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-35} & & \\\Leftrightarrow & x = \frac{-18}{35} & & \\ & V = \left\{ \frac{-18}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{245x} +63 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-30} \\\Leftrightarrow & 420x-245x& = & 63-30 \\\Leftrightarrow & \color{red}{175} x& = & 33 \\\Leftrightarrow & x = \frac{33}{175} & & \\ & V = \left\{ \frac{33}{175} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 378x+105x& = & 70+90 \\\Leftrightarrow & \color{red}{483} x& = & 160 \\\Leftrightarrow & x = \frac{160}{483} & & \\ & V = \left\{ \frac{160}{483} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{7})& = & -3x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-24} & = & \color{red}{-84x} +49 \\\Leftrightarrow & 280x \color{red}{-24} \color{blue}{+24} \color{blue}{+84x} & = & \color{red}{-84x} +49 \color{blue}{+84x} \color{blue}{+24} \\\Leftrightarrow & 280x+84x& = & 49+24 \\\Leftrightarrow & \color{red}{364} x& = & 73 \\\Leftrightarrow & x = \frac{73}{364} & & \\ & V = \left\{ \frac{73}{364} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{11})& = & 9x+\frac{3}{8} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+280} & = & \color{red}{792x} +33 \\\Leftrightarrow & -3080x \color{red}{+280} \color{blue}{-280} \color{blue}{-792x} & = & \color{red}{792x} +33 \color{blue}{-792x} \color{blue}{-280} \\\Leftrightarrow & -3080x-792x& = & 33-280 \\\Leftrightarrow & \color{red}{-3872} x& = & -247 \\\Leftrightarrow & x = \frac{-247}{-3872} & & \\\Leftrightarrow & x = \frac{247}{3872} & & \\ & V = \left\{ \frac{247}{3872} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{10}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+10} & = & \color{red}{-77x} +2 \\\Leftrightarrow & -66x \color{red}{+10} \color{blue}{-10} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-10} \\\Leftrightarrow & -66x+77x& = & 2-10 \\\Leftrightarrow & \color{red}{11} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{24x} +28 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +28 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 112x-24x& = & 28-21 \\\Leftrightarrow & \color{red}{88} x& = & 7 \\\Leftrightarrow & x = \frac{7}{88} & & \\ & V = \left\{ \frac{7}{88} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +4 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 4-12 \\\Leftrightarrow & \color{red}{-85} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-85} & & \\\Leftrightarrow & x = \frac{8}{85} & & \\ & V = \left\{ \frac{8}{85} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 30x-\frac{18}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-198} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 2310x \color{red}{-198} \color{blue}{+198} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+198} \\\Leftrightarrow & 2310x+539x& = & 42+198 \\\Leftrightarrow & \color{red}{2849} x& = & 240 \\\Leftrightarrow & x = \frac{240}{2849} & & \\ & V = \left\{ \frac{240}{2849} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+90} & = & \color{red}{-567x} +14 \\\Leftrightarrow & 1260x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +14 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & 1260x+567x& = & 14-90 \\\Leftrightarrow & \color{red}{1827} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{1827} & & \\ & V = \left\{ \frac{-76}{1827} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{11})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+72} & = & \color{red}{297x} +110 \\\Leftrightarrow & 1980x \color{red}{+72} \color{blue}{-72} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{-72} \\\Leftrightarrow & 1980x-297x& = & 110-72 \\\Leftrightarrow & \color{red}{1683} x& = & 38 \\\Leftrightarrow & x = \frac{38}{1683} & & \\ & V = \left\{ \frac{38}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-8} & = & \color{red}{-63x} +7 \\\Leftrightarrow & -54x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -54x+63x& = & 7+8 \\\Leftrightarrow & \color{red}{9} x& = & 15 \\\Leftrightarrow & x = \frac{15}{9} & & \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)