Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -60x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & -60x+70x& = & 45+24 \\\Leftrightarrow & \color{red}{10} x& = & 69 \\\Leftrightarrow & x = \frac{69}{10} & & \\ & V = \left\{ \frac{69}{10} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -6x+\frac{5}{6} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -6x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-36x} +5 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{+56} \\\Leftrightarrow & 210x+36x& = & 5+56 \\\Leftrightarrow & \color{red}{246} x& = & 61 \\\Leftrightarrow & x = \frac{61}{246} & & \\ & V = \left\{ \frac{61}{246} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+72} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 792x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 792x+165x& = & 22-72 \\\Leftrightarrow & \color{red}{957} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{957} & & \\ & V = \left\{ \frac{-50}{957} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -6x+\frac{12}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+24} & = & \color{red}{-98x} +49 \\\Leftrightarrow & -84x \color{red}{+24} \color{blue}{-24} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{-24} \\\Leftrightarrow & -84x+98x& = & 49-24 \\\Leftrightarrow & \color{red}{14} x& = & 25 \\\Leftrightarrow & x = \frac{25}{14} & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{7})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 24x+\frac{12}{7}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+132} & = & \color{red}{385x} +14 \\\Leftrightarrow & 1848x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +14 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1848x-385x& = & 14-132 \\\Leftrightarrow & \color{red}{1463} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{1463} & & \\ & V = \left\{ \frac{-118}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{6}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-42} & = & \color{red}{175x} +50 \\\Leftrightarrow & -315x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & -315x-175x& = & 50+42 \\\Leftrightarrow & \color{red}{-490} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-490} & & \\\Leftrightarrow & x = \frac{-46}{245} & & \\ & V = \left\{ \frac{-46}{245} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{7})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{9}{7}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{18}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{-56x} +21 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{+56x} & = & \color{red}{-56x} +21 \color{blue}{+56x} \color{blue}{+18} \\\Leftrightarrow & -210x+56x& = & 21+18 \\\Leftrightarrow & \color{red}{-154} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-154} & & \\\Leftrightarrow & x = \frac{-39}{154} & & \\ & V = \left\{ \frac{-39}{154} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+40} & = & \color{red}{75x} +24 \\\Leftrightarrow & 180x \color{red}{+40} \color{blue}{-40} \color{blue}{-75x} & = & \color{red}{75x} +24 \color{blue}{-75x} \color{blue}{-40} \\\Leftrightarrow & 180x-75x& = & 24-40 \\\Leftrightarrow & \color{red}{105} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{105} & & \\ & V = \left\{ \frac{-16}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{315x} +40 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & -280x-315x& = & 40+84 \\\Leftrightarrow & \color{red}{-595} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-595} & & \\\Leftrightarrow & x = \frac{-124}{595} & & \\ & V = \left\{ \frac{-124}{595} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{9})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+4} & = & \color{red}{-45x} +7 \\\Leftrightarrow & -36x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +7 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & -36x+45x& = & 7-4 \\\Leftrightarrow & \color{red}{9} x& = & 3 \\\Leftrightarrow & x = \frac{3}{9} & & \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{2})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{15}{2}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-105} & = & \color{red}{42x} +20 \\\Leftrightarrow & 140x \color{red}{-105} \color{blue}{+105} \color{blue}{-42x} & = & \color{red}{42x} +20 \color{blue}{-42x} \color{blue}{+105} \\\Leftrightarrow & 140x-42x& = & 20+105 \\\Leftrightarrow & \color{red}{98} x& = & 125 \\\Leftrightarrow & x = \frac{125}{98} & & \\ & V = \left\{ \frac{125}{98} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & 120x+105x& = & 18+40 \\\Leftrightarrow & \color{red}{225} x& = & 58 \\\Leftrightarrow & x = \frac{58}{225} & & \\ & V = \left\{ \frac{58}{225} \right\} & \\\end{align}\)