Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{5})& = & -4x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{21}{5}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x- \frac{126}{ \color{blue}{30} })& = & (\frac{-120}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{-126} & = & \color{red}{-120x} +25 \\\Leftrightarrow & 630x \color{red}{-126} \color{blue}{+126} \color{blue}{+120x} & = & \color{red}{-120x} +25 \color{blue}{+120x} \color{blue}{+126} \\\Leftrightarrow & 630x+120x& = & 25+126 \\\Leftrightarrow & \color{red}{750} x& = & 151 \\\Leftrightarrow & x = \frac{151}{750} & & \\ & V = \left\{ \frac{151}{750} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{8})& = & -2x+\frac{5}{12} \\\Leftrightarrow & 35x-\frac{35}{8}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x- \frac{105}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{-48x} +10 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{+48x} & = & \color{red}{-48x} +10 \color{blue}{+48x} \color{blue}{+105} \\\Leftrightarrow & 840x+48x& = & 10+105 \\\Leftrightarrow & \color{red}{888} x& = & 115 \\\Leftrightarrow & x = \frac{115}{888} & & \\ & V = \left\{ \frac{115}{888} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{2})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 28x+\frac{35}{2}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{+175} & = & \color{red}{-30x} +7 \\\Leftrightarrow & 280x \color{red}{+175} \color{blue}{-175} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{-175} \\\Leftrightarrow & 280x+30x& = & 7-175 \\\Leftrightarrow & \color{red}{310} x& = & -168 \\\Leftrightarrow & x = \frac{-168}{310} & & \\\Leftrightarrow & x = \frac{-84}{155} & & \\ & V = \left\{ \frac{-84}{155} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-30} & = & \color{red}{-175x} +21 \\\Leftrightarrow & 420x \color{red}{-30} \color{blue}{+30} \color{blue}{+175x} & = & \color{red}{-175x} +21 \color{blue}{+175x} \color{blue}{+30} \\\Leftrightarrow & 420x+175x& = & 21+30 \\\Leftrightarrow & \color{red}{595} x& = & 51 \\\Leftrightarrow & x = \frac{51}{595} & & \\\Leftrightarrow & x = \frac{3}{35} & & \\ & V = \left\{ \frac{3}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{-405x} +20 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{+405x} & = & \color{red}{-405x} +20 \color{blue}{+405x} \color{blue}{-36} \\\Leftrightarrow & -360x+405x& = & 20-36 \\\Leftrightarrow & \color{red}{45} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{45} & & \\ & V = \left\{ \frac{-16}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{-315x} +25 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{+315x} & = & \color{red}{-315x} +25 \color{blue}{+315x} \color{blue}{+36} \\\Leftrightarrow & -450x+315x& = & 25+36 \\\Leftrightarrow & \color{red}{-135} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-135} & & \\\Leftrightarrow & x = \frac{-61}{135} & & \\ & V = \left\{ \frac{-61}{135} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{3})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{-18x} +15 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{+18x} & = & \color{red}{-18x} +15 \color{blue}{+18x} \color{blue}{+16} \\\Leftrightarrow & 96x+18x& = & 15+16 \\\Leftrightarrow & \color{red}{114} x& = & 31 \\\Leftrightarrow & x = \frac{31}{114} & & \\ & V = \left\{ \frac{31}{114} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{2})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{9}{2}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{50x} +6 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{-50x} & = & \color{red}{50x} +6 \color{blue}{-50x} \color{blue}{-45} \\\Leftrightarrow & -120x-50x& = & 6-45 \\\Leftrightarrow & \color{red}{-170} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-170} & & \\\Leftrightarrow & x = \frac{39}{170} & & \\ & V = \left\{ \frac{39}{170} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 252x-105x& = & 56-18 \\\Leftrightarrow & \color{red}{147} x& = & 38 \\\Leftrightarrow & x = \frac{38}{147} & & \\ & V = \left\{ \frac{38}{147} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{3})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{25}{3}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{50}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-50} & = & \color{red}{-18x} +15 \\\Leftrightarrow & -120x \color{red}{-50} \color{blue}{+50} \color{blue}{+18x} & = & \color{red}{-18x} +15 \color{blue}{+18x} \color{blue}{+50} \\\Leftrightarrow & -120x+18x& = & 15+50 \\\Leftrightarrow & \color{red}{-102} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-102} & & \\\Leftrightarrow & x = \frac{-65}{102} & & \\ & V = \left\{ \frac{-65}{102} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & 300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 300x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{230} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{230} & & \\ & V = \left\{ \frac{-9}{230} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{11})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 16x+\frac{8}{11}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1408}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1408x \color{red}{+64} & = & \color{red}{-440x} +55 \\\Leftrightarrow & 1408x \color{red}{+64} \color{blue}{-64} \color{blue}{+440x} & = & \color{red}{-440x} +55 \color{blue}{+440x} \color{blue}{-64} \\\Leftrightarrow & 1408x+440x& = & 55-64 \\\Leftrightarrow & \color{red}{1848} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{1848} & & \\\Leftrightarrow & x = \frac{-3}{616} & & \\ & V = \left\{ \frac{-3}{616} \right\} & \\\end{align}\)