Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+32} & = & \color{red}{-42x} +35 \\\Leftrightarrow & -112x \color{red}{+32} \color{blue}{-32} \color{blue}{+42x} & = & \color{red}{-42x} +35 \color{blue}{+42x} \color{blue}{-32} \\\Leftrightarrow & -112x+42x& = & 35-32 \\\Leftrightarrow & \color{red}{-70} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-70} & & \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{6}{7} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-112x} +24 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+112x} & = & \color{red}{-112x} +24 \color{blue}{+112x} \color{blue}{-105} \\\Leftrightarrow & -420x+112x& = & 24-105 \\\Leftrightarrow & \color{red}{-308} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-308} & & \\\Leftrightarrow & x = \frac{81}{308} & & \\ & V = \left\{ \frac{81}{308} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{105x} +40 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & -450x-105x& = & 40-72 \\\Leftrightarrow & \color{red}{-555} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-555} & & \\\Leftrightarrow & x = \frac{32}{555} & & \\ & V = \left\{ \frac{32}{555} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{-175x} +14 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & -420x+175x& = & 14-150 \\\Leftrightarrow & \color{red}{-245} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-245} & & \\\Leftrightarrow & x = \frac{136}{245} & & \\ & V = \left\{ \frac{136}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{7})& = & 9x+\frac{3}{11} \\\Leftrightarrow & 8x-\frac{20}{7}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-220} & = & \color{red}{693x} +21 \\\Leftrightarrow & 616x \color{red}{-220} \color{blue}{+220} \color{blue}{-693x} & = & \color{red}{693x} +21 \color{blue}{-693x} \color{blue}{+220} \\\Leftrightarrow & 616x-693x& = & 21+220 \\\Leftrightarrow & \color{red}{-77} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-77} & & \\\Leftrightarrow & x = \frac{-241}{77} & & \\ & V = \left\{ \frac{-241}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{539x} +21 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & 1540x-539x& = & 21-220 \\\Leftrightarrow & \color{red}{1001} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{1001} & & \\ & V = \left\{ \frac{-199}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+18} \\\Leftrightarrow & 120x-50x& = & 45+18 \\\Leftrightarrow & \color{red}{70} x& = & 63 \\\Leftrightarrow & x = \frac{63}{70} & & \\\Leftrightarrow & x = \frac{9}{10} & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+66} & = & \color{red}{385x} +70 \\\Leftrightarrow & 462x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +70 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & 462x-385x& = & 70-66 \\\Leftrightarrow & \color{red}{77} x& = & 4 \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{9})& = & 2x+\frac{5}{12} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 2x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{72}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+80} & = & \color{red}{72x} +15 \\\Leftrightarrow & 540x \color{red}{+80} \color{blue}{-80} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{-80} \\\Leftrightarrow & 540x-72x& = & 15-80 \\\Leftrightarrow & \color{red}{468} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{468} & & \\\Leftrightarrow & x = \frac{-5}{36} & & \\ & V = \left\{ \frac{-5}{36} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{3})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{-147x} +27 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{+147x} & = & \color{red}{-147x} +27 \color{blue}{+147x} \color{blue}{+70} \\\Leftrightarrow & -210x+147x& = & 27+70 \\\Leftrightarrow & \color{red}{-63} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-63} & & \\\Leftrightarrow & x = \frac{-97}{63} & & \\ & V = \left\{ \frac{-97}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & 2x+\frac{7}{4} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 2x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+48} & = & \color{red}{40x} +35 \\\Leftrightarrow & 180x \color{red}{+48} \color{blue}{-48} \color{blue}{-40x} & = & \color{red}{40x} +35 \color{blue}{-40x} \color{blue}{-48} \\\Leftrightarrow & 180x-40x& = & 35-48 \\\Leftrightarrow & \color{red}{140} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{140} & & \\ & V = \left\{ \frac{-13}{140} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{11})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{20}{11}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{60}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-60} & = & \color{red}{-264x} +88 \\\Leftrightarrow & -495x \color{red}{-60} \color{blue}{+60} \color{blue}{+264x} & = & \color{red}{-264x} +88 \color{blue}{+264x} \color{blue}{+60} \\\Leftrightarrow & -495x+264x& = & 88+60 \\\Leftrightarrow & \color{red}{-231} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-231} & & \\\Leftrightarrow & x = \frac{-148}{231} & & \\ & V = \left\{ \frac{-148}{231} \right\} & \\\end{align}\)