Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{+40} & = & \color{red}{315x} +36 \\\Leftrightarrow & -720x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +36 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & -720x-315x& = & 36-40 \\\Leftrightarrow & \color{red}{-1035} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-1035} & & \\\Leftrightarrow & x = \frac{4}{1035} & & \\ & V = \left\{ \frac{4}{1035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+10} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & -42x-49x& = & 10-10 \\\Leftrightarrow & \color{red}{-91} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-91} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+54} \\\Leftrightarrow & 270x+225x& = & 50+54 \\\Leftrightarrow & \color{red}{495} x& = & 104 \\\Leftrightarrow & x = \frac{104}{495} & & \\ & V = \left\{ \frac{104}{495} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{8})& = & 8x+\frac{7}{8} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -168x \color{red}{+21} & = & \color{red}{64x} +7 \\\Leftrightarrow & -168x \color{red}{+21} \color{blue}{-21} \color{blue}{-64x} & = & \color{red}{64x} +7 \color{blue}{-64x} \color{blue}{-21} \\\Leftrightarrow & -168x-64x& = & 7-21 \\\Leftrightarrow & \color{red}{-232} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-232} & & \\\Leftrightarrow & x = \frac{7}{116} & & \\ & V = \left\{ \frac{7}{116} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+98} & = & \color{red}{42x} +30 \\\Leftrightarrow & 441x \color{red}{+98} \color{blue}{-98} \color{blue}{-42x} & = & \color{red}{42x} +30 \color{blue}{-42x} \color{blue}{-98} \\\Leftrightarrow & 441x-42x& = & 30-98 \\\Leftrightarrow & \color{red}{399} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{399} & & \\ & V = \left\{ \frac{-68}{399} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{20}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+220} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -770x-539x& = & 70-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{-1309} & & \\\Leftrightarrow & x = \frac{150}{1309} & & \\ & V = \left\{ \frac{150}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-56} & = & \color{red}{-441x} +90 \\\Leftrightarrow & -378x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +90 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & -378x+441x& = & 90+56 \\\Leftrightarrow & \color{red}{63} x& = & 146 \\\Leftrightarrow & x = \frac{146}{63} & & \\ & V = \left\{ \frac{146}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{+18} & = & \color{red}{99x} +5 \\\Leftrightarrow & -198x \color{red}{+18} \color{blue}{-18} \color{blue}{-99x} & = & \color{red}{99x} +5 \color{blue}{-99x} \color{blue}{-18} \\\Leftrightarrow & -198x-99x& = & 5-18 \\\Leftrightarrow & \color{red}{-297} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-297} & & \\\Leftrightarrow & x = \frac{13}{297} & & \\ & V = \left\{ \frac{13}{297} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-54} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -504x \color{red}{-54} \color{blue}{+54} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+54} \\\Leftrightarrow & -504x+189x& = & 28+54 \\\Leftrightarrow & \color{red}{-315} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-315} & & \\\Leftrightarrow & x = \frac{-82}{315} & & \\ & V = \left\{ \frac{-82}{315} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{16}{3}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-112} & = & \color{red}{63x} +12 \\\Leftrightarrow & -420x \color{red}{-112} \color{blue}{+112} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+112} \\\Leftrightarrow & -420x-63x& = & 12+112 \\\Leftrightarrow & \color{red}{-483} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-483} & & \\\Leftrightarrow & x = \frac{-124}{483} & & \\ & V = \left\{ \frac{-124}{483} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{-30x} +10 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{+30x} & = & \color{red}{-30x} +10 \color{blue}{+30x} \color{blue}{+36} \\\Leftrightarrow & 135x+30x& = & 10+36 \\\Leftrightarrow & \color{red}{165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{165} & & \\ & V = \left\{ \frac{46}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 280x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{105} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{105} & & \\ & V = \left\{ \frac{-74}{105} \right\} & \\\end{align}\)