Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 3x+\frac{5}{9} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 3x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-42} & = & \color{red}{27x} +5 \\\Leftrightarrow & 126x \color{red}{-42} \color{blue}{+42} \color{blue}{-27x} & = & \color{red}{27x} +5 \color{blue}{-27x} \color{blue}{+42} \\\Leftrightarrow & 126x-27x& = & 5+42 \\\Leftrightarrow & \color{red}{99} x& = & 47 \\\Leftrightarrow & x = \frac{47}{99} & & \\ & V = \left\{ \frac{47}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -9x+\frac{3}{11} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+308} & = & \color{red}{-297x} +9 \\\Leftrightarrow & 924x \color{red}{+308} \color{blue}{-308} \color{blue}{+297x} & = & \color{red}{-297x} +9 \color{blue}{+297x} \color{blue}{-308} \\\Leftrightarrow & 924x+297x& = & 9-308 \\\Leftrightarrow & \color{red}{1221} x& = & -299 \\\Leftrightarrow & x = \frac{-299}{1221} & & \\ & V = \left\{ \frac{-299}{1221} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-12} & = & \color{red}{55x} +5 \\\Leftrightarrow & -132x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & -132x-55x& = & 5+12 \\\Leftrightarrow & \color{red}{-187} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-187} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{10})& = & -2x+\frac{5}{12} \\\Leftrightarrow & 9x+\frac{9}{10}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 10 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{540}{ \color{blue}{60} }x+ \frac{54}{ \color{blue}{60} })& = & (\frac{-120}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 540x \color{red}{+54} & = & \color{red}{-120x} +25 \\\Leftrightarrow & 540x \color{red}{+54} \color{blue}{-54} \color{blue}{+120x} & = & \color{red}{-120x} +25 \color{blue}{+120x} \color{blue}{-54} \\\Leftrightarrow & 540x+120x& = & 25-54 \\\Leftrightarrow & \color{red}{660} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{660} & & \\ & V = \left\{ \frac{-29}{660} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{35x} +4 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 150x-35x& = & 4-12 \\\Leftrightarrow & \color{red}{115} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{115} & & \\ & V = \left\{ \frac{-8}{115} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & -6x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{10}{11}& = & -6x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-70} & = & \color{red}{-462x} +110 \\\Leftrightarrow & 1925x \color{red}{-70} \color{blue}{+70} \color{blue}{+462x} & = & \color{red}{-462x} +110 \color{blue}{+462x} \color{blue}{+70} \\\Leftrightarrow & 1925x+462x& = & 110+70 \\\Leftrightarrow & \color{red}{2387} x& = & 180 \\\Leftrightarrow & x = \frac{180}{2387} & & \\ & V = \left\{ \frac{180}{2387} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-385x} +25 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 660x+385x& = & 25+132 \\\Leftrightarrow & \color{red}{1045} x& = & 157 \\\Leftrightarrow & x = \frac{157}{1045} & & \\ & V = \left\{ \frac{157}{1045} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -6x+\frac{8}{3} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -6x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-60} & = & \color{red}{-126x} +56 \\\Leftrightarrow & 525x \color{red}{-60} \color{blue}{+60} \color{blue}{+126x} & = & \color{red}{-126x} +56 \color{blue}{+126x} \color{blue}{+60} \\\Leftrightarrow & 525x+126x& = & 56+60 \\\Leftrightarrow & \color{red}{651} x& = & 116 \\\Leftrightarrow & x = \frac{116}{651} & & \\ & V = \left\{ \frac{116}{651} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -14x-\frac{35}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-245} & = & \color{red}{-63x} +9 \\\Leftrightarrow & -294x \color{red}{-245} \color{blue}{+245} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{+245} \\\Leftrightarrow & -294x+63x& = & 9+245 \\\Leftrightarrow & \color{red}{-231} x& = & 254 \\\Leftrightarrow & x = \frac{254}{-231} & & \\\Leftrightarrow & x = \frac{-254}{231} & & \\ & V = \left\{ \frac{-254}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{9})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x-\frac{20}{9}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{-80} & = & \color{red}{180x} +21 \\\Leftrightarrow & -432x \color{red}{-80} \color{blue}{+80} \color{blue}{-180x} & = & \color{red}{180x} +21 \color{blue}{-180x} \color{blue}{+80} \\\Leftrightarrow & -432x-180x& = & 21+80 \\\Leftrightarrow & \color{red}{-612} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-612} & & \\\Leftrightarrow & x = \frac{-101}{612} & & \\ & V = \left\{ \frac{-101}{612} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+18} & = & \color{red}{168x} +70 \\\Leftrightarrow & -315x \color{red}{+18} \color{blue}{-18} \color{blue}{-168x} & = & \color{red}{168x} +70 \color{blue}{-168x} \color{blue}{-18} \\\Leftrightarrow & -315x-168x& = & 70-18 \\\Leftrightarrow & \color{red}{-483} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-483} & & \\\Leftrightarrow & x = \frac{-52}{483} & & \\ & V = \left\{ \frac{-52}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{11})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{8}{11}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-24} & = & \color{red}{-99x} +110 \\\Leftrightarrow & -660x \color{red}{-24} \color{blue}{+24} \color{blue}{+99x} & = & \color{red}{-99x} +110 \color{blue}{+99x} \color{blue}{+24} \\\Leftrightarrow & -660x+99x& = & 110+24 \\\Leftrightarrow & \color{red}{-561} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-561} & & \\\Leftrightarrow & x = \frac{-134}{561} & & \\ & V = \left\{ \frac{-134}{561} \right\} & \\\end{align}\)