Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+88} & = & \color{red}{-99x} +15 \\\Leftrightarrow & 264x \color{red}{+88} \color{blue}{-88} \color{blue}{+99x} & = & \color{red}{-99x} +15 \color{blue}{+99x} \color{blue}{-88} \\\Leftrightarrow & 264x+99x& = & 15-88 \\\Leftrightarrow & \color{red}{363} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{363} & & \\ & V = \left\{ \frac{-73}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{+60} \\\Leftrightarrow & -420x+63x& = & 56+60 \\\Leftrightarrow & \color{red}{-357} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-357} & & \\\Leftrightarrow & x = \frac{-116}{357} & & \\ & V = \left\{ \frac{-116}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -4x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{-108} & = & \color{red}{-180x} +10 \\\Leftrightarrow & 675x \color{red}{-108} \color{blue}{+108} \color{blue}{+180x} & = & \color{red}{-180x} +10 \color{blue}{+180x} \color{blue}{+108} \\\Leftrightarrow & 675x+180x& = & 10+108 \\\Leftrightarrow & \color{red}{855} x& = & 118 \\\Leftrightarrow & x = \frac{118}{855} & & \\ & V = \left\{ \frac{118}{855} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{63x} +30 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -90x-63x& = & 30+8 \\\Leftrightarrow & \color{red}{-153} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-153} & & \\\Leftrightarrow & x = \frac{-38}{153} & & \\ & V = \left\{ \frac{-38}{153} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{24}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-216} & = & \color{red}{495x} +110 \\\Leftrightarrow & 1188x \color{red}{-216} \color{blue}{+216} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+216} \\\Leftrightarrow & 1188x-495x& = & 110+216 \\\Leftrightarrow & \color{red}{693} x& = & 326 \\\Leftrightarrow & x = \frac{326}{693} & & \\ & V = \left\{ \frac{326}{693} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 126x-105x& = & 70-18 \\\Leftrightarrow & \color{red}{21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{+189} & = & \color{red}{-216x} +16 \\\Leftrightarrow & -1008x \color{red}{+189} \color{blue}{-189} \color{blue}{+216x} & = & \color{red}{-216x} +16 \color{blue}{+216x} \color{blue}{-189} \\\Leftrightarrow & -1008x+216x& = & 16-189 \\\Leftrightarrow & \color{red}{-792} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-792} & & \\\Leftrightarrow & x = \frac{173}{792} & & \\ & V = \left\{ \frac{173}{792} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{11})& = & -2x+\frac{3}{10} \\\Leftrightarrow & 21x+\frac{14}{11}& = & -2x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2310}{ \color{blue}{110} }x+ \frac{140}{ \color{blue}{110} })& = & (\frac{-220}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2310x \color{red}{+140} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 2310x \color{red}{+140} \color{blue}{-140} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-140} \\\Leftrightarrow & 2310x+220x& = & 33-140 \\\Leftrightarrow & \color{red}{2530} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{2530} & & \\ & V = \left\{ \frac{-107}{2530} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{10})& = & -8x+\frac{2}{5} \\\Leftrightarrow & -21x+\frac{21}{10}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-210}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -210x \color{red}{+21} & = & \color{red}{-80x} +4 \\\Leftrightarrow & -210x \color{red}{+21} \color{blue}{-21} \color{blue}{+80x} & = & \color{red}{-80x} +4 \color{blue}{+80x} \color{blue}{-21} \\\Leftrightarrow & -210x+80x& = & 4-21 \\\Leftrightarrow & \color{red}{-130} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-130} & & \\\Leftrightarrow & x = \frac{17}{130} & & \\ & V = \left\{ \frac{17}{130} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{20}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-20} & = & \color{red}{21x} +10 \\\Leftrightarrow & 36x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 36x-21x& = & 10+20 \\\Leftrightarrow & \color{red}{15} x& = & 30 \\\Leftrightarrow & x = \frac{30}{15} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{8})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 28x+\frac{35}{8}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x+ \frac{35}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{+35} & = & \color{red}{40x} +36 \\\Leftrightarrow & 224x \color{red}{+35} \color{blue}{-35} \color{blue}{-40x} & = & \color{red}{40x} +36 \color{blue}{-40x} \color{blue}{-35} \\\Leftrightarrow & 224x-40x& = & 36-35 \\\Leftrightarrow & \color{red}{184} x& = & 1 \\\Leftrightarrow & x = \frac{1}{184} & & \\ & V = \left\{ \frac{1}{184} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{60x} +40 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{+36} \\\Leftrightarrow & -225x-60x& = & 40+36 \\\Leftrightarrow & \color{red}{-285} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-285} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)