Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 360x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{285} x& = & 4 \\\Leftrightarrow & x = \frac{4}{285} & & \\ & V = \left\{ \frac{4}{285} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{9})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x+\frac{8}{9}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+88} & = & \color{red}{-495x} +45 \\\Leftrightarrow & 1188x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +45 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & 1188x+495x& = & 45-88 \\\Leftrightarrow & \color{red}{1683} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{1683} & & \\ & V = \left\{ \frac{-43}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+54} & = & \color{red}{693x} +55 \\\Leftrightarrow & 990x \color{red}{+54} \color{blue}{-54} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{-54} \\\Leftrightarrow & 990x-693x& = & 55-54 \\\Leftrightarrow & \color{red}{297} x& = & 1 \\\Leftrightarrow & x = \frac{1}{297} & & \\ & V = \left\{ \frac{1}{297} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{175}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-175} & = & \color{red}{165x} +22 \\\Leftrightarrow & 1540x \color{red}{-175} \color{blue}{+175} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+175} \\\Leftrightarrow & 1540x-165x& = & 22+175 \\\Leftrightarrow & \color{red}{1375} x& = & 197 \\\Leftrightarrow & x = \frac{197}{1375} & & \\ & V = \left\{ \frac{197}{1375} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{7}{11} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+176} & = & \color{red}{-693x} +49 \\\Leftrightarrow & -616x \color{red}{+176} \color{blue}{-176} \color{blue}{+693x} & = & \color{red}{-693x} +49 \color{blue}{+693x} \color{blue}{-176} \\\Leftrightarrow & -616x+693x& = & 49-176 \\\Leftrightarrow & \color{red}{77} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{77} & & \\ & V = \left\{ \frac{-127}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{10}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{-10} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 66x \color{red}{-10} \color{blue}{+10} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{+10} \\\Leftrightarrow & 66x+77x& = & 2+10 \\\Leftrightarrow & \color{red}{143} x& = & 12 \\\Leftrightarrow & x = \frac{12}{143} & & \\ & V = \left\{ \frac{12}{143} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{16}{3}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-48} & = & \color{red}{45x} +8 \\\Leftrightarrow & 108x \color{red}{-48} \color{blue}{+48} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{+48} \\\Leftrightarrow & 108x-45x& = & 8+48 \\\Leftrightarrow & \color{red}{63} x& = & 56 \\\Leftrightarrow & x = \frac{56}{63} & & \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{3})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{-200} & = & \color{red}{-270x} +27 \\\Leftrightarrow & -600x \color{red}{-200} \color{blue}{+200} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{+200} \\\Leftrightarrow & -600x+270x& = & 27+200 \\\Leftrightarrow & \color{red}{-330} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-330} & & \\\Leftrightarrow & x = \frac{-227}{330} & & \\ & V = \left\{ \frac{-227}{330} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{9})& = & -8x+\frac{5}{11} \\\Leftrightarrow & -21x+\frac{14}{9}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{+154} & = & \color{red}{-792x} +45 \\\Leftrightarrow & -2079x \color{red}{+154} \color{blue}{-154} \color{blue}{+792x} & = & \color{red}{-792x} +45 \color{blue}{+792x} \color{blue}{-154} \\\Leftrightarrow & -2079x+792x& = & 45-154 \\\Leftrightarrow & \color{red}{-1287} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1287} & & \\\Leftrightarrow & x = \frac{109}{1287} & & \\ & V = \left\{ \frac{109}{1287} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{11})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 25x+\frac{10}{11}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+70} & = & \color{red}{-154x} +88 \\\Leftrightarrow & 1925x \color{red}{+70} \color{blue}{-70} \color{blue}{+154x} & = & \color{red}{-154x} +88 \color{blue}{+154x} \color{blue}{-70} \\\Leftrightarrow & 1925x+154x& = & 88-70 \\\Leftrightarrow & \color{red}{2079} x& = & 18 \\\Leftrightarrow & x = \frac{18}{2079} & & \\\Leftrightarrow & x = \frac{2}{231} & & \\ & V = \left\{ \frac{2}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & -8x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{14}{5}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-42} & = & \color{red}{-120x} +50 \\\Leftrightarrow & 315x \color{red}{-42} \color{blue}{+42} \color{blue}{+120x} & = & \color{red}{-120x} +50 \color{blue}{+120x} \color{blue}{+42} \\\Leftrightarrow & 315x+120x& = & 50+42 \\\Leftrightarrow & \color{red}{435} x& = & 92 \\\Leftrightarrow & x = \frac{92}{435} & & \\ & V = \left\{ \frac{92}{435} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{2})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{25}{2}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-275} & = & \color{red}{154x} +12 \\\Leftrightarrow & -220x \color{red}{-275} \color{blue}{+275} \color{blue}{-154x} & = & \color{red}{154x} +12 \color{blue}{-154x} \color{blue}{+275} \\\Leftrightarrow & -220x-154x& = & 12+275 \\\Leftrightarrow & \color{red}{-374} x& = & 287 \\\Leftrightarrow & x = \frac{287}{-374} & & \\\Leftrightarrow & x = \frac{-287}{374} & & \\ & V = \left\{ \frac{-287}{374} \right\} & \\\end{align}\)