Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{+270} & = & \color{red}{315x} +56 \\\Leftrightarrow & 1134x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & 1134x-315x& = & 56-270 \\\Leftrightarrow & \color{red}{819} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{819} & & \\ & V = \left\{ \frac{-214}{819} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{-255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-255} & & \\\Leftrightarrow & x = \frac{-86}{255} & & \\ & V = \left\{ \frac{-86}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{7})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 18x-\frac{18}{7}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-198} & = & \color{red}{-385x} +63 \\\Leftrightarrow & 1386x \color{red}{-198} \color{blue}{+198} \color{blue}{+385x} & = & \color{red}{-385x} +63 \color{blue}{+385x} \color{blue}{+198} \\\Leftrightarrow & 1386x+385x& = & 63+198 \\\Leftrightarrow & \color{red}{1771} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1771} & & \\ & V = \left\{ \frac{261}{1771} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{25}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{25}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-25} & = & \color{red}{-27x} +12 \\\Leftrightarrow & 180x \color{red}{-25} \color{blue}{+25} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{+25} \\\Leftrightarrow & 180x+27x& = & 12+25 \\\Leftrightarrow & \color{red}{207} x& = & 37 \\\Leftrightarrow & x = \frac{37}{207} & & \\ & V = \left\{ \frac{37}{207} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 6x+\frac{10}{7}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 420x \color{red}{+100} & = & \color{red}{-350x} +21 \\\Leftrightarrow & 420x \color{red}{+100} \color{blue}{-100} \color{blue}{+350x} & = & \color{red}{-350x} +21 \color{blue}{+350x} \color{blue}{-100} \\\Leftrightarrow & 420x+350x& = & 21-100 \\\Leftrightarrow & \color{red}{770} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{770} & & \\ & V = \left\{ \frac{-79}{770} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{3})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+56} & = & \color{red}{108x} +9 \\\Leftrightarrow & -420x \color{red}{+56} \color{blue}{-56} \color{blue}{-108x} & = & \color{red}{108x} +9 \color{blue}{-108x} \color{blue}{-56} \\\Leftrightarrow & -420x-108x& = & 9-56 \\\Leftrightarrow & \color{red}{-528} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-528} & & \\\Leftrightarrow & x = \frac{47}{528} & & \\ & V = \left\{ \frac{47}{528} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-70} & = & \color{red}{120x} +18 \\\Leftrightarrow & 315x \color{red}{-70} \color{blue}{+70} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{+70} \\\Leftrightarrow & 315x-120x& = & 18+70 \\\Leftrightarrow & \color{red}{195} x& = & 88 \\\Leftrightarrow & x = \frac{88}{195} & & \\ & V = \left\{ \frac{88}{195} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{8})& = & 4x+\frac{4}{11} \\\Leftrightarrow & 21x-\frac{35}{8}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{-385} & = & \color{red}{352x} +32 \\\Leftrightarrow & 1848x \color{red}{-385} \color{blue}{+385} \color{blue}{-352x} & = & \color{red}{352x} +32 \color{blue}{-352x} \color{blue}{+385} \\\Leftrightarrow & 1848x-352x& = & 32+385 \\\Leftrightarrow & \color{red}{1496} x& = & 417 \\\Leftrightarrow & x = \frac{417}{1496} & & \\ & V = \left\{ \frac{417}{1496} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 5x+\frac{7}{4} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -112x \color{red}{+24} & = & \color{red}{140x} +49 \\\Leftrightarrow & -112x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +49 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & -112x-140x& = & 49-24 \\\Leftrightarrow & \color{red}{-252} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-252} & & \\\Leftrightarrow & x = \frac{-25}{252} & & \\ & V = \left\{ \frac{-25}{252} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{8}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+88} & = & \color{red}{385x} +10 \\\Leftrightarrow & -330x \color{red}{+88} \color{blue}{-88} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{-88} \\\Leftrightarrow & -330x-385x& = & 10-88 \\\Leftrightarrow & \color{red}{-715} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-715} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+88} & = & \color{red}{693x} +81 \\\Leftrightarrow & -594x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +81 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & -594x-693x& = & 81-88 \\\Leftrightarrow & \color{red}{-1287} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-1287} & & \\\Leftrightarrow & x = \frac{7}{1287} & & \\ & V = \left\{ \frac{7}{1287} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{504}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 504x \color{red}{+120} & = & \color{red}{294x} +35 \\\Leftrightarrow & 504x \color{red}{+120} \color{blue}{-120} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-120} \\\Leftrightarrow & 504x-294x& = & 35-120 \\\Leftrightarrow & \color{red}{210} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{210} & & \\\Leftrightarrow & x = \frac{-17}{42} & & \\ & V = \left\{ \frac{-17}{42} \right\} & \\\end{align}\)