Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{2})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{15}{2}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-12}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -12x \color{red}{-15} & = & \color{red}{-14x} +9 \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+14x} & = & \color{red}{-14x} +9 \color{blue}{+14x} \color{blue}{+15} \\\Leftrightarrow & -12x+14x& = & 9+15 \\\Leftrightarrow & \color{red}{2} x& = & 24 \\\Leftrightarrow & x = \frac{24}{2} & & \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{-63} & = & \color{red}{-48x} +16 \\\Leftrightarrow & 840x \color{red}{-63} \color{blue}{+63} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{+63} \\\Leftrightarrow & 840x+48x& = & 16+63 \\\Leftrightarrow & \color{red}{888} x& = & 79 \\\Leftrightarrow & x = \frac{79}{888} & & \\ & V = \left\{ \frac{79}{888} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x- \frac{32}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{-32} & = & \color{red}{280x} +35 \\\Leftrightarrow & -240x \color{red}{-32} \color{blue}{+32} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+32} \\\Leftrightarrow & -240x-280x& = & 35+32 \\\Leftrightarrow & \color{red}{-520} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-520} & & \\\Leftrightarrow & x = \frac{-67}{520} & & \\ & V = \left\{ \frac{-67}{520} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & -9x+\frac{5}{8} \\\Leftrightarrow & -8x+\frac{10}{3}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -192x \color{red}{+80} & = & \color{red}{-216x} +15 \\\Leftrightarrow & -192x \color{red}{+80} \color{blue}{-80} \color{blue}{+216x} & = & \color{red}{-216x} +15 \color{blue}{+216x} \color{blue}{-80} \\\Leftrightarrow & -192x+216x& = & 15-80 \\\Leftrightarrow & \color{red}{24} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{24} & & \\ & V = \left\{ \frac{-65}{24} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-10} & = & \color{red}{-49x} +2 \\\Leftrightarrow & -175x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +2 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -175x+49x& = & 2+10 \\\Leftrightarrow & \color{red}{-126} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-126} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{4})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -35x+\frac{35}{4}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{105}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{108x} +8 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{-108x} & = & \color{red}{108x} +8 \color{blue}{-108x} \color{blue}{-105} \\\Leftrightarrow & -420x-108x& = & 8-105 \\\Leftrightarrow & \color{red}{-528} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-528} & & \\\Leftrightarrow & x = \frac{97}{528} & & \\ & V = \left\{ \frac{97}{528} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{4})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{25}{4}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+175} & = & \color{red}{-84x} +40 \\\Leftrightarrow & -560x \color{red}{+175} \color{blue}{-175} \color{blue}{+84x} & = & \color{red}{-84x} +40 \color{blue}{+84x} \color{blue}{-175} \\\Leftrightarrow & -560x+84x& = & 40-175 \\\Leftrightarrow & \color{red}{-476} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{-476} & & \\\Leftrightarrow & x = \frac{135}{476} & & \\ & V = \left\{ \frac{135}{476} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{+15} & = & \color{red}{-28x} +5 \\\Leftrightarrow & -40x \color{red}{+15} \color{blue}{-15} \color{blue}{+28x} & = & \color{red}{-28x} +5 \color{blue}{+28x} \color{blue}{-15} \\\Leftrightarrow & -40x+28x& = & 5-15 \\\Leftrightarrow & \color{red}{-12} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-12} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +2 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 2+10 \\\Leftrightarrow & \color{red}{-119} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-119} & & \\\Leftrightarrow & x = \frac{-12}{119} & & \\ & V = \left\{ \frac{-12}{119} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{7})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 18x+\frac{24}{7}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1008}{ \color{blue}{56} }x+ \frac{192}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1008x \color{red}{+192} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 1008x \color{red}{+192} \color{blue}{-192} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{-192} \\\Leftrightarrow & 1008x+280x& = & 35-192 \\\Leftrightarrow & \color{red}{1288} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{1288} & & \\ & V = \left\{ \frac{-157}{1288} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{9})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{16}{9}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{176}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+176} & = & \color{red}{-693x} +72 \\\Leftrightarrow & 1980x \color{red}{+176} \color{blue}{-176} \color{blue}{+693x} & = & \color{red}{-693x} +72 \color{blue}{+693x} \color{blue}{-176} \\\Leftrightarrow & 1980x+693x& = & 72-176 \\\Leftrightarrow & \color{red}{2673} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{2673} & & \\ & V = \left\{ \frac{-104}{2673} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+36} & = & \color{red}{60x} +20 \\\Leftrightarrow & -225x \color{red}{+36} \color{blue}{-36} \color{blue}{-60x} & = & \color{red}{60x} +20 \color{blue}{-60x} \color{blue}{-36} \\\Leftrightarrow & -225x-60x& = & 20-36 \\\Leftrightarrow & \color{red}{-285} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-285} & & \\\Leftrightarrow & x = \frac{16}{285} & & \\ & V = \left\{ \frac{16}{285} \right\} & \\\end{align}\)