Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{165x} +44 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & 396x-165x& = & 44-54 \\\Leftrightarrow & \color{red}{231} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{231} & & \\ & V = \left\{ \frac{-10}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{9})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x+\frac{20}{9}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+140} & = & \color{red}{315x} +72 \\\Leftrightarrow & -756x \color{red}{+140} \color{blue}{-140} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{-140} \\\Leftrightarrow & -756x-315x& = & 72-140 \\\Leftrightarrow & \color{red}{-1071} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1071} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -4x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+20} & = & \color{red}{-56x} +63 \\\Leftrightarrow & 350x \color{red}{+20} \color{blue}{-20} \color{blue}{+56x} & = & \color{red}{-56x} +63 \color{blue}{+56x} \color{blue}{-20} \\\Leftrightarrow & 350x+56x& = & 63-20 \\\Leftrightarrow & \color{red}{406} x& = & 43 \\\Leftrightarrow & x = \frac{43}{406} & & \\ & V = \left\{ \frac{43}{406} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{6})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 21x+\frac{35}{6}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+35} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 126x \color{red}{+35} \color{blue}{-35} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{-35} \\\Leftrightarrow & 126x+12x& = & 9-35 \\\Leftrightarrow & \color{red}{138} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{138} & & \\\Leftrightarrow & x = \frac{-13}{69} & & \\ & V = \left\{ \frac{-13}{69} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-108} & = & \color{red}{225x} +40 \\\Leftrightarrow & 270x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & 270x-225x& = & 40+108 \\\Leftrightarrow & \color{red}{45} x& = & 148 \\\Leftrightarrow & x = \frac{148}{45} & & \\ & V = \left\{ \frac{148}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{4}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-189x} +30 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{+28} \\\Leftrightarrow & 210x+189x& = & 30+28 \\\Leftrightarrow & \color{red}{399} x& = & 58 \\\Leftrightarrow & x = \frac{58}{399} & & \\ & V = \left\{ \frac{58}{399} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{3})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 4x+\frac{4}{3}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{+16} & = & \color{red}{84x} +27 \\\Leftrightarrow & 48x \color{red}{+16} \color{blue}{-16} \color{blue}{-84x} & = & \color{red}{84x} +27 \color{blue}{-84x} \color{blue}{-16} \\\Leftrightarrow & 48x-84x& = & 27-16 \\\Leftrightarrow & \color{red}{-36} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-36} & & \\\Leftrightarrow & x = \frac{-11}{36} & & \\ & V = \left\{ \frac{-11}{36} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{+140} & = & \color{red}{-150x} +21 \\\Leftrightarrow & 840x \color{red}{+140} \color{blue}{-140} \color{blue}{+150x} & = & \color{red}{-150x} +21 \color{blue}{+150x} \color{blue}{-140} \\\Leftrightarrow & 840x+150x& = & 21-140 \\\Leftrightarrow & \color{red}{990} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{990} & & \\ & V = \left\{ \frac{-119}{990} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{11})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{-693x} +55 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{+693x} & = & \color{red}{-693x} +55 \color{blue}{+693x} \color{blue}{-90} \\\Leftrightarrow & 990x+693x& = & 55-90 \\\Leftrightarrow & \color{red}{1683} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{1683} & & \\ & V = \left\{ \frac{-35}{1683} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{3})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{10}{3}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{-147x} +6 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{+147x} & = & \color{red}{-147x} +6 \color{blue}{+147x} \color{blue}{-70} \\\Leftrightarrow & -210x+147x& = & 6-70 \\\Leftrightarrow & \color{red}{-63} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-63} & & \\\Leftrightarrow & x = \frac{64}{63} & & \\ & V = \left\{ \frac{64}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{-12} \\\Leftrightarrow & 120x+75x& = & 10-12 \\\Leftrightarrow & \color{red}{195} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{195} & & \\ & V = \left\{ \frac{-2}{195} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-176} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 924x \color{red}{-176} \color{blue}{+176} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+176} \\\Leftrightarrow & 924x+385x& = & 70+176 \\\Leftrightarrow & \color{red}{1309} x& = & 246 \\\Leftrightarrow & x = \frac{246}{1309} & & \\ & V = \left\{ \frac{246}{1309} \right\} & \\\end{align}\)