Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-20} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -84x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & -84x+98x& = & 35+20 \\\Leftrightarrow & \color{red}{14} x& = & 55 \\\Leftrightarrow & x = \frac{55}{14} & & \\ & V = \left\{ \frac{55}{14} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-108} & = & \color{red}{315x} +40 \\\Leftrightarrow & 1350x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & 1350x-315x& = & 40+108 \\\Leftrightarrow & \color{red}{1035} x& = & 148 \\\Leftrightarrow & x = \frac{148}{1035} & & \\ & V = \left\{ \frac{148}{1035} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{3})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 4x-\frac{10}{3}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{-20} & = & \color{red}{-18x} +21 \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+18x} & = & \color{red}{-18x} +21 \color{blue}{+18x} \color{blue}{+20} \\\Leftrightarrow & 24x+18x& = & 21+20 \\\Leftrightarrow & \color{red}{42} x& = & 41 \\\Leftrightarrow & x = \frac{41}{42} & & \\ & V = \left\{ \frac{41}{42} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-192} & = & \color{red}{200x} +35 \\\Leftrightarrow & 480x \color{red}{-192} \color{blue}{+192} \color{blue}{-200x} & = & \color{red}{200x} +35 \color{blue}{-200x} \color{blue}{+192} \\\Leftrightarrow & 480x-200x& = & 35+192 \\\Leftrightarrow & \color{red}{280} x& = & 227 \\\Leftrightarrow & x = \frac{227}{280} & & \\ & V = \left\{ \frac{227}{280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -4x+\frac{10}{3} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{-60x} +50 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{+60x} & = & \color{red}{-60x} +50 \color{blue}{+60x} \color{blue}{-36} \\\Leftrightarrow & -270x+60x& = & 50-36 \\\Leftrightarrow & \color{red}{-210} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-210} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{11})& = & -2x+\frac{2}{3} \\\Leftrightarrow & -28x+\frac{14}{11}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{42}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+42} & = & \color{red}{-66x} +22 \\\Leftrightarrow & -924x \color{red}{+42} \color{blue}{-42} \color{blue}{+66x} & = & \color{red}{-66x} +22 \color{blue}{+66x} \color{blue}{-42} \\\Leftrightarrow & -924x+66x& = & 22-42 \\\Leftrightarrow & \color{red}{-858} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-858} & & \\\Leftrightarrow & x = \frac{10}{429} & & \\ & V = \left\{ \frac{10}{429} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{3})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{10}{3}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-70} & = & \color{red}{147x} +24 \\\Leftrightarrow & 168x \color{red}{-70} \color{blue}{+70} \color{blue}{-147x} & = & \color{red}{147x} +24 \color{blue}{-147x} \color{blue}{+70} \\\Leftrightarrow & 168x-147x& = & 24+70 \\\Leftrightarrow & \color{red}{21} x& = & 94 \\\Leftrightarrow & x = \frac{94}{21} & & \\ & V = \left\{ \frac{94}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -4x+\frac{6}{5}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-80}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{-180x} +45 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{+180x} & = & \color{red}{-180x} +45 \color{blue}{+180x} \color{blue}{-24} \\\Leftrightarrow & -80x+180x& = & 45-24 \\\Leftrightarrow & \color{red}{100} x& = & 21 \\\Leftrightarrow & x = \frac{21}{100} & & \\ & V = \left\{ \frac{21}{100} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{-385x} +20 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1650x+385x& = & 20+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1265} & & \\\Leftrightarrow & x = \frac{-152}{1265} & & \\ & V = \left\{ \frac{-152}{1265} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -4x+\frac{3}{10} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -4x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} })& = & (\frac{-440}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{+60} & = & \color{red}{-440x} +33 \\\Leftrightarrow & -1650x \color{red}{+60} \color{blue}{-60} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{-60} \\\Leftrightarrow & -1650x+440x& = & 33-60 \\\Leftrightarrow & \color{red}{-1210} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-1210} & & \\\Leftrightarrow & x = \frac{27}{1210} & & \\ & V = \left\{ \frac{27}{1210} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & 3x+\frac{10}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{264x} +80 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{-264x} & = & \color{red}{264x} +80 \color{blue}{-264x} \color{blue}{+231} \\\Leftrightarrow & -1232x-264x& = & 80+231 \\\Leftrightarrow & \color{red}{-1496} x& = & 311 \\\Leftrightarrow & x = \frac{311}{-1496} & & \\\Leftrightarrow & x = \frac{-311}{1496} & & \\ & V = \left\{ \frac{-311}{1496} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{16}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+80} & = & \color{red}{-175x} +28 \\\Leftrightarrow & -420x \color{red}{+80} \color{blue}{-80} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-80} \\\Leftrightarrow & -420x+175x& = & 28-80 \\\Leftrightarrow & \color{red}{-245} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-245} & & \\\Leftrightarrow & x = \frac{52}{245} & & \\ & V = \left\{ \frac{52}{245} \right\} & \\\end{align}\)