Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -28x+63x& = & 4+10 \\\Leftrightarrow & \color{red}{35} x& = & 14 \\\Leftrightarrow & x = \frac{14}{35} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{10}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x- \frac{80}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+80} \\\Leftrightarrow & 240x+72x& = & 21+80 \\\Leftrightarrow & \color{red}{312} x& = & 101 \\\Leftrightarrow & x = \frac{101}{312} & & \\ & V = \left\{ \frac{101}{312} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+28} & = & \color{red}{-315x} +30 \\\Leftrightarrow & -280x \color{red}{+28} \color{blue}{-28} \color{blue}{+315x} & = & \color{red}{-315x} +30 \color{blue}{+315x} \color{blue}{-28} \\\Leftrightarrow & -280x+315x& = & 30-28 \\\Leftrightarrow & \color{red}{35} x& = & 2 \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +35 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 35-36 \\\Leftrightarrow & \color{red}{255} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{255} & & \\ & V = \left\{ \frac{-1}{255} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{9})& = & 9x+\frac{2}{11} \\\Leftrightarrow & -25x+\frac{25}{9}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x+ \frac{275}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{+275} & = & \color{red}{891x} +18 \\\Leftrightarrow & -2475x \color{red}{+275} \color{blue}{-275} \color{blue}{-891x} & = & \color{red}{891x} +18 \color{blue}{-891x} \color{blue}{-275} \\\Leftrightarrow & -2475x-891x& = & 18-275 \\\Leftrightarrow & \color{red}{-3366} x& = & -257 \\\Leftrightarrow & x = \frac{-257}{-3366} & & \\\Leftrightarrow & x = \frac{257}{3366} & & \\ & V = \left\{ \frac{257}{3366} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x-\frac{35}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-105} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -462x \color{red}{-105} \color{blue}{+105} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{+105} \\\Leftrightarrow & -462x+99x& = & 44+105 \\\Leftrightarrow & \color{red}{-363} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-363} & & \\\Leftrightarrow & x = \frac{-149}{363} & & \\ & V = \left\{ \frac{-149}{363} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{+16} & = & \color{red}{162x} +63 \\\Leftrightarrow & -144x \color{red}{+16} \color{blue}{-16} \color{blue}{-162x} & = & \color{red}{162x} +63 \color{blue}{-162x} \color{blue}{-16} \\\Leftrightarrow & -144x-162x& = & 63-16 \\\Leftrightarrow & \color{red}{-306} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-306} & & \\\Leftrightarrow & x = \frac{-47}{306} & & \\ & V = \left\{ \frac{-47}{306} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{21}{11}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-63} & = & \color{red}{-264x} +88 \\\Leftrightarrow & -693x \color{red}{-63} \color{blue}{+63} \color{blue}{+264x} & = & \color{red}{-264x} +88 \color{blue}{+264x} \color{blue}{+63} \\\Leftrightarrow & -693x+264x& = & 88+63 \\\Leftrightarrow & \color{red}{-429} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-429} & & \\\Leftrightarrow & x = \frac{-151}{429} & & \\ & V = \left\{ \frac{-151}{429} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{7})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 20x-\frac{8}{7}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{64}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-64} & = & \color{red}{392x} +21 \\\Leftrightarrow & 1120x \color{red}{-64} \color{blue}{+64} \color{blue}{-392x} & = & \color{red}{392x} +21 \color{blue}{-392x} \color{blue}{+64} \\\Leftrightarrow & 1120x-392x& = & 21+64 \\\Leftrightarrow & \color{red}{728} x& = & 85 \\\Leftrightarrow & x = \frac{85}{728} & & \\ & V = \left\{ \frac{85}{728} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -90x+63x& = & 4+8 \\\Leftrightarrow & \color{red}{-27} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-27} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{6}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{135x} +40 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{+18} \\\Leftrightarrow & 120x-135x& = & 40+18 \\\Leftrightarrow & \color{red}{-15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-15} & & \\\Leftrightarrow & x = \frac{-58}{15} & & \\ & V = \left\{ \frac{-58}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{28}{9}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+28} & = & \color{red}{-45x} +24 \\\Leftrightarrow & -126x \color{red}{+28} \color{blue}{-28} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{-28} \\\Leftrightarrow & -126x+45x& = & 24-28 \\\Leftrightarrow & \color{red}{-81} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-81} & & \\\Leftrightarrow & x = \frac{4}{81} & & \\ & V = \left\{ \frac{4}{81} \right\} & \\\end{align}\)