Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+110} & = & \color{red}{539x} +70 \\\Leftrightarrow & -462x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -462x-539x& = & 70-110 \\\Leftrightarrow & \color{red}{-1001} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1001} & & \\\Leftrightarrow & x = \frac{40}{1001} & & \\ & V = \left\{ \frac{40}{1001} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & 6x+\frac{8}{9} \\\Leftrightarrow & 35x-\frac{21}{8}& = & 6x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2520}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{432}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2520x \color{red}{-189} & = & \color{red}{432x} +64 \\\Leftrightarrow & 2520x \color{red}{-189} \color{blue}{+189} \color{blue}{-432x} & = & \color{red}{432x} +64 \color{blue}{-432x} \color{blue}{+189} \\\Leftrightarrow & 2520x-432x& = & 64+189 \\\Leftrightarrow & \color{red}{2088} x& = & 253 \\\Leftrightarrow & x = \frac{253}{2088} & & \\ & V = \left\{ \frac{253}{2088} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-6} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -70x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -70x+49x& = & 9+6 \\\Leftrightarrow & \color{red}{-21} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-21} & & \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{18}{5}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+54} & = & \color{red}{75x} +25 \\\Leftrightarrow & 180x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +25 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & 180x-75x& = & 25-54 \\\Leftrightarrow & \color{red}{105} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{105} & & \\ & V = \left\{ \frac{-29}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{8}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-56} & = & \color{red}{-147x} +12 \\\Leftrightarrow & -336x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & -336x+147x& = & 12+56 \\\Leftrightarrow & \color{red}{-189} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-189} & & \\\Leftrightarrow & x = \frac{-68}{189} & & \\ & V = \left\{ \frac{-68}{189} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -24x-\frac{30}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1584}{ \color{blue}{66} }x- \frac{180}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1584x \color{red}{-180} & = & \color{red}{330x} +55 \\\Leftrightarrow & -1584x \color{red}{-180} \color{blue}{+180} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{+180} \\\Leftrightarrow & -1584x-330x& = & 55+180 \\\Leftrightarrow & \color{red}{-1914} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-1914} & & \\\Leftrightarrow & x = \frac{-235}{1914} & & \\ & V = \left\{ \frac{-235}{1914} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{9})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{10}{9}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-10} & = & \color{red}{27x} +30 \\\Leftrightarrow & 90x \color{red}{-10} \color{blue}{+10} \color{blue}{-27x} & = & \color{red}{27x} +30 \color{blue}{-27x} \color{blue}{+10} \\\Leftrightarrow & 90x-27x& = & 30+10 \\\Leftrightarrow & \color{red}{63} x& = & 40 \\\Leftrightarrow & x = \frac{40}{63} & & \\ & V = \left\{ \frac{40}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{5})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 35x+\frac{14}{5}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{20x} +35 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{-20x} & = & \color{red}{20x} +35 \color{blue}{-20x} \color{blue}{-28} \\\Leftrightarrow & 350x-20x& = & 35-28 \\\Leftrightarrow & \color{red}{330} x& = & 7 \\\Leftrightarrow & x = \frac{7}{330} & & \\ & V = \left\{ \frac{7}{330} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{-48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 160x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & 160x+100x& = & 45+48 \\\Leftrightarrow & \color{red}{260} x& = & 93 \\\Leftrightarrow & x = \frac{93}{260} & & \\ & V = \left\{ \frac{93}{260} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{35}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+105} & = & \color{red}{-99x} +88 \\\Leftrightarrow & -1155x \color{red}{+105} \color{blue}{-105} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{-105} \\\Leftrightarrow & -1155x+99x& = & 88-105 \\\Leftrightarrow & \color{red}{-1056} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1056} & & \\\Leftrightarrow & x = \frac{17}{1056} & & \\ & V = \left\{ \frac{17}{1056} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{8})& = & -4x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -4x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-160}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{-160x} +16 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{+160x} & = & \color{red}{-160x} +16 \color{blue}{+160x} \color{blue}{+105} \\\Leftrightarrow & 840x+160x& = & 16+105 \\\Leftrightarrow & \color{red}{1000} x& = & 121 \\\Leftrightarrow & x = \frac{121}{1000} & & \\ & V = \left\{ \frac{121}{1000} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{4})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{9}{4}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x- \frac{27}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{-27} & = & \color{red}{-84x} +40 \\\Leftrightarrow & -72x \color{red}{-27} \color{blue}{+27} \color{blue}{+84x} & = & \color{red}{-84x} +40 \color{blue}{+84x} \color{blue}{+27} \\\Leftrightarrow & -72x+84x& = & 40+27 \\\Leftrightarrow & \color{red}{12} x& = & 67 \\\Leftrightarrow & x = \frac{67}{12} & & \\ & V = \left\{ \frac{67}{12} \right\} & \\\end{align}\)