Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 20-132 \\\Leftrightarrow & \color{red}{935} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{935} & & \\ & V = \left\{ \frac{-112}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-672}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -672x \color{red}{+120} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -672x \color{red}{+120} \color{blue}{-120} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-120} \\\Leftrightarrow & -672x+140x& = & 63-120 \\\Leftrightarrow & \color{red}{-532} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-532} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{1}{2})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{5}{2}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{250}{ \color{blue}{10} }x- \frac{25}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 250x \color{red}{-25} & = & \color{red}{-20x} +12 \\\Leftrightarrow & 250x \color{red}{-25} \color{blue}{+25} \color{blue}{+20x} & = & \color{red}{-20x} +12 \color{blue}{+20x} \color{blue}{+25} \\\Leftrightarrow & 250x+20x& = & 12+25 \\\Leftrightarrow & \color{red}{270} x& = & 37 \\\Leftrightarrow & x = \frac{37}{270} & & \\ & V = \left\{ \frac{37}{270} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{9x} +8 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{+14} \\\Leftrightarrow & -105x-9x& = & 8+14 \\\Leftrightarrow & \color{red}{-114} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-114} & & \\\Leftrightarrow & x = \frac{-11}{57} & & \\ & V = \left\{ \frac{-11}{57} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{25}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{75}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+75} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -420x \color{red}{+75} \color{blue}{-75} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-75} \\\Leftrightarrow & -420x+147x& = & 14-75 \\\Leftrightarrow & \color{red}{-273} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-273} & & \\\Leftrightarrow & x = \frac{61}{273} & & \\ & V = \left\{ \frac{61}{273} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{-63x} +9 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{+56} \\\Leftrightarrow & 84x+63x& = & 9+56 \\\Leftrightarrow & \color{red}{147} x& = & 65 \\\Leftrightarrow & x = \frac{65}{147} & & \\ & V = \left\{ \frac{65}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+84} & = & \color{red}{-280x} +45 \\\Leftrightarrow & -525x \color{red}{+84} \color{blue}{-84} \color{blue}{+280x} & = & \color{red}{-280x} +45 \color{blue}{+280x} \color{blue}{-84} \\\Leftrightarrow & -525x+280x& = & 45-84 \\\Leftrightarrow & \color{red}{-245} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-245} & & \\\Leftrightarrow & x = \frac{39}{245} & & \\ & V = \left\{ \frac{39}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 6x+\frac{10}{11} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{198x} +30 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-198x} & = & \color{red}{198x} +30 \color{blue}{-198x} \color{blue}{-154} \\\Leftrightarrow & -1155x-198x& = & 30-154 \\\Leftrightarrow & \color{red}{-1353} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{-1353} & & \\\Leftrightarrow & x = \frac{124}{1353} & & \\ & V = \left\{ \frac{124}{1353} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-72} & = & \color{red}{105x} +40 \\\Leftrightarrow & 450x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & 450x-105x& = & 40+72 \\\Leftrightarrow & \color{red}{345} x& = & 112 \\\Leftrightarrow & x = \frac{112}{345} & & \\ & V = \left\{ \frac{112}{345} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & -9x+\frac{9}{8} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1440}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1440x \color{red}{+64} & = & \color{red}{-648x} +81 \\\Leftrightarrow & 1440x \color{red}{+64} \color{blue}{-64} \color{blue}{+648x} & = & \color{red}{-648x} +81 \color{blue}{+648x} \color{blue}{-64} \\\Leftrightarrow & 1440x+648x& = & 81-64 \\\Leftrightarrow & \color{red}{2088} x& = & 17 \\\Leftrightarrow & x = \frac{17}{2088} & & \\ & V = \left\{ \frac{17}{2088} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{6})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 25x+\frac{25}{6}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1050}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1050x \color{red}{+175} & = & \color{red}{-294x} +54 \\\Leftrightarrow & 1050x \color{red}{+175} \color{blue}{-175} \color{blue}{+294x} & = & \color{red}{-294x} +54 \color{blue}{+294x} \color{blue}{-175} \\\Leftrightarrow & 1050x+294x& = & 54-175 \\\Leftrightarrow & \color{red}{1344} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{1344} & & \\ & V = \left\{ \frac{-121}{1344} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & 4x+\frac{9}{5} \\\Leftrightarrow & -15x+\frac{10}{3}& = & 4x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+50} & = & \color{red}{60x} +27 \\\Leftrightarrow & -225x \color{red}{+50} \color{blue}{-50} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{-50} \\\Leftrightarrow & -225x-60x& = & 27-50 \\\Leftrightarrow & \color{red}{-285} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-285} & & \\\Leftrightarrow & x = \frac{23}{285} & & \\ & V = \left\{ \frac{23}{285} \right\} & \\\end{align}\)