Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{-175x} +49 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{+175x} & = & \color{red}{-175x} +49 \color{blue}{+175x} \color{blue}{-30} \\\Leftrightarrow & 420x+175x& = & 49-30 \\\Leftrightarrow & \color{red}{595} x& = & 19 \\\Leftrightarrow & x = \frac{19}{595} & & \\ & V = \left\{ \frac{19}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{11})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -18x-\frac{12}{11}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{-96} & = & \color{red}{-792x} +77 \\\Leftrightarrow & -1584x \color{red}{-96} \color{blue}{+96} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+96} \\\Leftrightarrow & -1584x+792x& = & 77+96 \\\Leftrightarrow & \color{red}{-792} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-792} & & \\\Leftrightarrow & x = \frac{-173}{792} & & \\ & V = \left\{ \frac{-173}{792} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{8})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{-45} & = & \color{red}{120x} +10 \\\Leftrightarrow & 288x \color{red}{-45} \color{blue}{+45} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{+45} \\\Leftrightarrow & 288x-120x& = & 10+45 \\\Leftrightarrow & \color{red}{168} x& = & 55 \\\Leftrightarrow & x = \frac{55}{168} & & \\ & V = \left\{ \frac{55}{168} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-800}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -800x \color{red}{+75} & = & \color{red}{-280x} +16 \\\Leftrightarrow & -800x \color{red}{+75} \color{blue}{-75} \color{blue}{+280x} & = & \color{red}{-280x} +16 \color{blue}{+280x} \color{blue}{-75} \\\Leftrightarrow & -800x+280x& = & 16-75 \\\Leftrightarrow & \color{red}{-520} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-520} & & \\\Leftrightarrow & x = \frac{59}{520} & & \\ & V = \left\{ \frac{59}{520} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{16}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+112} & = & \color{red}{385x} +33 \\\Leftrightarrow & -924x \color{red}{+112} \color{blue}{-112} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{-112} \\\Leftrightarrow & -924x-385x& = & 33-112 \\\Leftrightarrow & \color{red}{-1309} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-1309} & & \\\Leftrightarrow & x = \frac{79}{1309} & & \\ & V = \left\{ \frac{79}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+60} & = & \color{red}{81x} +7 \\\Leftrightarrow & 180x \color{red}{+60} \color{blue}{-60} \color{blue}{-81x} & = & \color{red}{81x} +7 \color{blue}{-81x} \color{blue}{-60} \\\Leftrightarrow & 180x-81x& = & 7-60 \\\Leftrightarrow & \color{red}{99} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{99} & & \\ & V = \left\{ \frac{-53}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{135}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+135} & = & \color{red}{693x} +110 \\\Leftrightarrow & -594x \color{red}{+135} \color{blue}{-135} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-135} \\\Leftrightarrow & -594x-693x& = & 110-135 \\\Leftrightarrow & \color{red}{-1287} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-1287} & & \\\Leftrightarrow & x = \frac{25}{1287} & & \\ & V = \left\{ \frac{25}{1287} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{35x} +3 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & -90x-35x& = & 3+24 \\\Leftrightarrow & \color{red}{-125} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-125} & & \\\Leftrightarrow & x = \frac{-27}{125} & & \\ & V = \left\{ \frac{-27}{125} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{6})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 35x-\frac{35}{6}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{2310}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 2310x \color{red}{-385} & = & \color{red}{-198x} +60 \\\Leftrightarrow & 2310x \color{red}{-385} \color{blue}{+385} \color{blue}{+198x} & = & \color{red}{-198x} +60 \color{blue}{+198x} \color{blue}{+385} \\\Leftrightarrow & 2310x+198x& = & 60+385 \\\Leftrightarrow & \color{red}{2508} x& = & 445 \\\Leftrightarrow & x = \frac{445}{2508} & & \\ & V = \left\{ \frac{445}{2508} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{21}{11}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-770}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -770x \color{red}{-42} & = & \color{red}{-198x} +77 \\\Leftrightarrow & -770x \color{red}{-42} \color{blue}{+42} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{+42} \\\Leftrightarrow & -770x+198x& = & 77+42 \\\Leftrightarrow & \color{red}{-572} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-572} & & \\\Leftrightarrow & x = \frac{-119}{572} & & \\ & V = \left\{ \frac{-119}{572} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{11})& = & -6x+\frac{2}{3} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -6x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-105} & = & \color{red}{-198x} +22 \\\Leftrightarrow & -1155x \color{red}{-105} \color{blue}{+105} \color{blue}{+198x} & = & \color{red}{-198x} +22 \color{blue}{+198x} \color{blue}{+105} \\\Leftrightarrow & -1155x+198x& = & 22+105 \\\Leftrightarrow & \color{red}{-957} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-957} & & \\\Leftrightarrow & x = \frac{-127}{957} & & \\ & V = \left\{ \frac{-127}{957} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{8})& = & -2x+\frac{5}{6} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{-48x} +20 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +20 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 504x+48x& = & 20-63 \\\Leftrightarrow & \color{red}{552} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{552} & & \\ & V = \left\{ \frac{-43}{552} \right\} & \\\end{align}\)