Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-30} & = & \color{red}{84x} +28 \\\Leftrightarrow & 315x \color{red}{-30} \color{blue}{+30} \color{blue}{-84x} & = & \color{red}{84x} +28 \color{blue}{-84x} \color{blue}{+30} \\\Leftrightarrow & 315x-84x& = & 28+30 \\\Leftrightarrow & \color{red}{231} x& = & 58 \\\Leftrightarrow & x = \frac{58}{231} & & \\ & V = \left\{ \frac{58}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -4x+\frac{8}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+56} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -308x \color{red}{+56} \color{blue}{-56} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-56} \\\Leftrightarrow & -308x+385x& = & 22-56 \\\Leftrightarrow & \color{red}{77} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{77} & & \\ & V = \left\{ \frac{-34}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{6}{5}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{48}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-48} & = & \color{red}{200x} +35 \\\Leftrightarrow & -480x \color{red}{-48} \color{blue}{+48} \color{blue}{-200x} & = & \color{red}{200x} +35 \color{blue}{-200x} \color{blue}{+48} \\\Leftrightarrow & -480x-200x& = & 35+48 \\\Leftrightarrow & \color{red}{-680} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-680} & & \\\Leftrightarrow & x = \frac{-83}{680} & & \\ & V = \left\{ \frac{-83}{680} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{-60} & = & \color{red}{490x} +21 \\\Leftrightarrow & 280x \color{red}{-60} \color{blue}{+60} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+60} \\\Leftrightarrow & 280x-490x& = & 21+60 \\\Leftrightarrow & \color{red}{-210} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-210} & & \\\Leftrightarrow & x = \frac{-27}{70} & & \\ & V = \left\{ \frac{-27}{70} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{+32} & = & \color{red}{84x} +21 \\\Leftrightarrow & -240x \color{red}{+32} \color{blue}{-32} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{-32} \\\Leftrightarrow & -240x-84x& = & 21-32 \\\Leftrightarrow & \color{red}{-324} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-324} & & \\\Leftrightarrow & x = \frac{11}{324} & & \\ & V = \left\{ \frac{11}{324} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{-36x} +16 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{+36x} & = & \color{red}{-36x} +16 \color{blue}{+36x} \color{blue}{+45} \\\Leftrightarrow & -240x+36x& = & 16+45 \\\Leftrightarrow & \color{red}{-204} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-204} & & \\\Leftrightarrow & x = \frac{-61}{204} & & \\ & V = \left\{ \frac{-61}{204} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-16} \\\Leftrightarrow & 36x+15x& = & 8-16 \\\Leftrightarrow & \color{red}{51} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{51} & & \\ & V = \left\{ \frac{-8}{51} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -90x+63x& = & 10+8 \\\Leftrightarrow & \color{red}{-27} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-27} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{-110x} +77 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{-48} \\\Leftrightarrow & 396x+110x& = & 77-48 \\\Leftrightarrow & \color{red}{506} x& = & 29 \\\Leftrightarrow & x = \frac{29}{506} & & \\ & V = \left\{ \frac{29}{506} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 10 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-360}{ \color{blue}{60} }x+ \frac{54}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -360x \color{red}{+54} & = & \color{red}{-420x} +25 \\\Leftrightarrow & -360x \color{red}{+54} \color{blue}{-54} \color{blue}{+420x} & = & \color{red}{-420x} +25 \color{blue}{+420x} \color{blue}{-54} \\\Leftrightarrow & -360x+420x& = & 25-54 \\\Leftrightarrow & \color{red}{60} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{60} & & \\ & V = \left\{ \frac{-29}{60} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & 4x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-10} & = & \color{red}{28x} +8 \\\Leftrightarrow & 105x \color{red}{-10} \color{blue}{+10} \color{blue}{-28x} & = & \color{red}{28x} +8 \color{blue}{-28x} \color{blue}{+10} \\\Leftrightarrow & 105x-28x& = & 8+10 \\\Leftrightarrow & \color{red}{77} x& = & 18 \\\Leftrightarrow & x = \frac{18}{77} & & \\ & V = \left\{ \frac{18}{77} \right\} & \\\end{align}\)