Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{9})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 21x-\frac{28}{9}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-28} & = & \color{red}{-18x} +24 \\\Leftrightarrow & 189x \color{red}{-28} \color{blue}{+28} \color{blue}{+18x} & = & \color{red}{-18x} +24 \color{blue}{+18x} \color{blue}{+28} \\\Leftrightarrow & 189x+18x& = & 24+28 \\\Leftrightarrow & \color{red}{207} x& = & 52 \\\Leftrightarrow & x = \frac{52}{207} & & \\ & V = \left\{ \frac{52}{207} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{11})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{28}{11}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-84} & = & \color{red}{-297x} +110 \\\Leftrightarrow & 462x \color{red}{-84} \color{blue}{+84} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+84} \\\Leftrightarrow & 462x+297x& = & 110+84 \\\Leftrightarrow & \color{red}{759} x& = & 194 \\\Leftrightarrow & x = \frac{194}{759} & & \\ & V = \left\{ \frac{194}{759} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{-100} & = & \color{red}{30x} +24 \\\Leftrightarrow & 375x \color{red}{-100} \color{blue}{+100} \color{blue}{-30x} & = & \color{red}{30x} +24 \color{blue}{-30x} \color{blue}{+100} \\\Leftrightarrow & 375x-30x& = & 24+100 \\\Leftrightarrow & \color{red}{345} x& = & 124 \\\Leftrightarrow & x = \frac{124}{345} & & \\ & V = \left\{ \frac{124}{345} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-21} & = & \color{red}{-40x} +20 \\\Leftrightarrow & 112x \color{red}{-21} \color{blue}{+21} \color{blue}{+40x} & = & \color{red}{-40x} +20 \color{blue}{+40x} \color{blue}{+21} \\\Leftrightarrow & 112x+40x& = & 20+21 \\\Leftrightarrow & \color{red}{152} x& = & 41 \\\Leftrightarrow & x = \frac{41}{152} & & \\ & V = \left\{ \frac{41}{152} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+96} & = & \color{red}{-280x} +15 \\\Leftrightarrow & 240x \color{red}{+96} \color{blue}{-96} \color{blue}{+280x} & = & \color{red}{-280x} +15 \color{blue}{+280x} \color{blue}{-96} \\\Leftrightarrow & 240x+280x& = & 15-96 \\\Leftrightarrow & \color{red}{520} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{520} & & \\ & V = \left\{ \frac{-81}{520} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-12} & = & \color{red}{-42x} +63 \\\Leftrightarrow & 112x \color{red}{-12} \color{blue}{+12} \color{blue}{+42x} & = & \color{red}{-42x} +63 \color{blue}{+42x} \color{blue}{+12} \\\Leftrightarrow & 112x+42x& = & 63+12 \\\Leftrightarrow & \color{red}{154} x& = & 75 \\\Leftrightarrow & x = \frac{75}{154} & & \\ & V = \left\{ \frac{75}{154} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-20} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -70x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -70x+49x& = & 10+20 \\\Leftrightarrow & \color{red}{-21} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-21} & & \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{10}{3}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+50} & = & \color{red}{135x} +12 \\\Leftrightarrow & -120x \color{red}{+50} \color{blue}{-50} \color{blue}{-135x} & = & \color{red}{135x} +12 \color{blue}{-135x} \color{blue}{-50} \\\Leftrightarrow & -120x-135x& = & 12-50 \\\Leftrightarrow & \color{red}{-255} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-255} & & \\\Leftrightarrow & x = \frac{38}{255} & & \\ & V = \left\{ \frac{38}{255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x+ \frac{96}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{+96} & = & \color{red}{-280x} +49 \\\Leftrightarrow & 672x \color{red}{+96} \color{blue}{-96} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{-96} \\\Leftrightarrow & 672x+280x& = & 49-96 \\\Leftrightarrow & \color{red}{952} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{952} & & \\ & V = \left\{ \frac{-47}{952} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 4x+\frac{7}{11} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-132} & = & \color{red}{220x} +35 \\\Leftrightarrow & -825x \color{red}{-132} \color{blue}{+132} \color{blue}{-220x} & = & \color{red}{220x} +35 \color{blue}{-220x} \color{blue}{+132} \\\Leftrightarrow & -825x-220x& = & 35+132 \\\Leftrightarrow & \color{red}{-1045} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-1045} & & \\\Leftrightarrow & x = \frac{-167}{1045} & & \\ & V = \left\{ \frac{-167}{1045} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x- \frac{70}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{-70} & = & \color{red}{90x} +15 \\\Leftrightarrow & -252x \color{red}{-70} \color{blue}{+70} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+70} \\\Leftrightarrow & -252x-90x& = & 15+70 \\\Leftrightarrow & \color{red}{-342} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-342} & & \\\Leftrightarrow & x = \frac{-85}{342} & & \\ & V = \left\{ \frac{-85}{342} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{3})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{-64} & = & \color{red}{216x} +21 \\\Leftrightarrow & 192x \color{red}{-64} \color{blue}{+64} \color{blue}{-216x} & = & \color{red}{216x} +21 \color{blue}{-216x} \color{blue}{+64} \\\Leftrightarrow & 192x-216x& = & 21+64 \\\Leftrightarrow & \color{red}{-24} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-24} & & \\\Leftrightarrow & x = \frac{-85}{24} & & \\ & V = \left\{ \frac{-85}{24} \right\} & \\\end{align}\)