Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+54} & = & \color{red}{315x} +40 \\\Leftrightarrow & -270x \color{red}{+54} \color{blue}{-54} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-54} \\\Leftrightarrow & -270x-315x& = & 40-54 \\\Leftrightarrow & \color{red}{-585} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-585} & & \\\Leftrightarrow & x = \frac{14}{585} & & \\ & V = \left\{ \frac{14}{585} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & -90x+25x& = & 8+12 \\\Leftrightarrow & \color{red}{-65} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-65} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{-32} & = & \color{red}{-36x} +9 \\\Leftrightarrow & 96x \color{red}{-32} \color{blue}{+32} \color{blue}{+36x} & = & \color{red}{-36x} +9 \color{blue}{+36x} \color{blue}{+32} \\\Leftrightarrow & 96x+36x& = & 9+32 \\\Leftrightarrow & \color{red}{132} x& = & 41 \\\Leftrightarrow & x = \frac{41}{132} & & \\ & V = \left\{ \frac{41}{132} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & -8x+\frac{5}{3} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -8x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-63} & = & \color{red}{-264x} +55 \\\Leftrightarrow & 693x \color{red}{-63} \color{blue}{+63} \color{blue}{+264x} & = & \color{red}{-264x} +55 \color{blue}{+264x} \color{blue}{+63} \\\Leftrightarrow & 693x+264x& = & 55+63 \\\Leftrightarrow & \color{red}{957} x& = & 118 \\\Leftrightarrow & x = \frac{118}{957} & & \\ & V = \left\{ \frac{118}{957} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+1)& = & -5x+\frac{9}{10} \\\Leftrightarrow & -28x-7& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x- \frac{70}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{-70} & = & \color{red}{-50x} +9 \\\Leftrightarrow & -280x \color{red}{-70} \color{blue}{+70} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+70} \\\Leftrightarrow & -280x+50x& = & 9+70 \\\Leftrightarrow & \color{red}{-230} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-230} & & \\\Leftrightarrow & x = \frac{-79}{230} & & \\ & V = \left\{ \frac{-79}{230} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 7x+\frac{7}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{539x} +49 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +49 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -1540x-539x& = & 49-110 \\\Leftrightarrow & \color{red}{-2079} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-2079} & & \\\Leftrightarrow & x = \frac{61}{2079} & & \\ & V = \left\{ \frac{61}{2079} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{385x} +14 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +14 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1848x-385x& = & 14+330 \\\Leftrightarrow & \color{red}{1463} x& = & 344 \\\Leftrightarrow & x = \frac{344}{1463} & & \\ & V = \left\{ \frac{344}{1463} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{16}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-80} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 700x \color{red}{-80} \color{blue}{+80} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+80} \\\Leftrightarrow & 700x+245x& = & 42+80 \\\Leftrightarrow & \color{red}{945} x& = & 122 \\\Leftrightarrow & x = \frac{122}{945} & & \\ & V = \left\{ \frac{122}{945} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1188}{ \color{blue}{66} }x+ \frac{108}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1188x \color{red}{+108} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 1188x \color{red}{+108} \color{blue}{-108} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{-108} \\\Leftrightarrow & 1188x+330x& = & 77-108 \\\Leftrightarrow & \color{red}{1518} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{1518} & & \\ & V = \left\{ \frac{-31}{1518} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{16}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-112} & = & \color{red}{189x} +6 \\\Leftrightarrow & -168x \color{red}{-112} \color{blue}{+112} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{+112} \\\Leftrightarrow & -168x-189x& = & 6+112 \\\Leftrightarrow & \color{red}{-357} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-357} & & \\\Leftrightarrow & x = \frac{-118}{357} & & \\ & V = \left\{ \frac{-118}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1008}{ \color{blue}{84} }x+ \frac{240}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1008x \color{red}{+240} & = & \color{red}{-588x} +35 \\\Leftrightarrow & 1008x \color{red}{+240} \color{blue}{-240} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{-240} \\\Leftrightarrow & 1008x+588x& = & 35-240 \\\Leftrightarrow & \color{red}{1596} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{1596} & & \\ & V = \left\{ \frac{-205}{1596} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & -8x+\frac{8}{5} \\\Leftrightarrow & 21x+\frac{35}{2}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+175} & = & \color{red}{-80x} +16 \\\Leftrightarrow & 210x \color{red}{+175} \color{blue}{-175} \color{blue}{+80x} & = & \color{red}{-80x} +16 \color{blue}{+80x} \color{blue}{-175} \\\Leftrightarrow & 210x+80x& = & 16-175 \\\Leftrightarrow & \color{red}{290} x& = & -159 \\\Leftrightarrow & x = \frac{-159}{290} & & \\ & V = \left\{ \frac{-159}{290} \right\} & \\\end{align}\)