Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+90} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 1260x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & 1260x+441x& = & 14-90 \\\Leftrightarrow & \color{red}{1701} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{1701} & & \\ & V = \left\{ \frac{-76}{1701} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-24} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -60x \color{red}{-24} \color{blue}{+24} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+24} \\\Leftrightarrow & -60x+25x& = & 6+24 \\\Leftrightarrow & \color{red}{-35} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-35} & & \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{8}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-24} & = & \color{red}{-75x} +10 \\\Leftrightarrow & -180x \color{red}{-24} \color{blue}{+24} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+24} \\\Leftrightarrow & -180x+75x& = & 10+24 \\\Leftrightarrow & \color{red}{-105} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-105} & & \\\Leftrightarrow & x = \frac{-34}{105} & & \\ & V = \left\{ \frac{-34}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+48} & = & \color{red}{-140x} +25 \\\Leftrightarrow & -120x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +25 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & -120x+140x& = & 25-48 \\\Leftrightarrow & \color{red}{20} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{20} & & \\ & V = \left\{ \frac{-23}{20} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-126} & = & \color{red}{385x} +99 \\\Leftrightarrow & -924x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & -924x-385x& = & 99+126 \\\Leftrightarrow & \color{red}{-1309} x& = & 225 \\\Leftrightarrow & x = \frac{225}{-1309} & & \\\Leftrightarrow & x = \frac{-225}{1309} & & \\ & V = \left\{ \frac{-225}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 28x+\frac{35}{4}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{560}{ \color{blue}{20} }x+ \frac{175}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 560x \color{red}{+175} & = & \color{red}{180x} +6 \\\Leftrightarrow & 560x \color{red}{+175} \color{blue}{-175} \color{blue}{-180x} & = & \color{red}{180x} +6 \color{blue}{-180x} \color{blue}{-175} \\\Leftrightarrow & 560x-180x& = & 6-175 \\\Leftrightarrow & \color{red}{380} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{380} & & \\ & V = \left\{ \frac{-169}{380} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -8x+\frac{2}{5} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+9} & = & \color{red}{-40x} +2 \\\Leftrightarrow & 75x \color{red}{+9} \color{blue}{-9} \color{blue}{+40x} & = & \color{red}{-40x} +2 \color{blue}{+40x} \color{blue}{-9} \\\Leftrightarrow & 75x+40x& = & 2-9 \\\Leftrightarrow & \color{red}{115} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{115} & & \\ & V = \left\{ \frac{-7}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{8})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{9}{8}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+9} & = & \color{red}{-40x} +20 \\\Leftrightarrow & -96x \color{red}{+9} \color{blue}{-9} \color{blue}{+40x} & = & \color{red}{-40x} +20 \color{blue}{+40x} \color{blue}{-9} \\\Leftrightarrow & -96x+40x& = & 20-9 \\\Leftrightarrow & \color{red}{-56} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-56} & & \\\Leftrightarrow & x = \frac{-11}{56} & & \\ & V = \left\{ \frac{-11}{56} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{105x} +12 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{+56} \\\Leftrightarrow & 84x-105x& = & 12+56 \\\Leftrightarrow & \color{red}{-21} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-21} & & \\\Leftrightarrow & x = \frac{-68}{21} & & \\ & V = \left\{ \frac{-68}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{6}{11}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-6} & = & \color{red}{-55x} +8 \\\Leftrightarrow & -132x \color{red}{-6} \color{blue}{+6} \color{blue}{+55x} & = & \color{red}{-55x} +8 \color{blue}{+55x} \color{blue}{+6} \\\Leftrightarrow & -132x+55x& = & 8+6 \\\Leftrightarrow & \color{red}{-77} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-77} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -12x+\frac{16}{11}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+80} & = & \color{red}{-275x} +99 \\\Leftrightarrow & -660x \color{red}{+80} \color{blue}{-80} \color{blue}{+275x} & = & \color{red}{-275x} +99 \color{blue}{+275x} \color{blue}{-80} \\\Leftrightarrow & -660x+275x& = & 99-80 \\\Leftrightarrow & \color{red}{-385} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-385} & & \\\Leftrightarrow & x = \frac{-19}{385} & & \\ & V = \left\{ \frac{-19}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 7+12 \\\Leftrightarrow & \color{red}{-115} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-115} & & \\\Leftrightarrow & x = \frac{-19}{115} & & \\ & V = \left\{ \frac{-19}{115} \right\} & \\\end{align}\)