Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{30}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-150} & = & \color{red}{495x} +66 \\\Leftrightarrow & -990x \color{red}{-150} \color{blue}{+150} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{+150} \\\Leftrightarrow & -990x-495x& = & 66+150 \\\Leftrightarrow & \color{red}{-1485} x& = & 216 \\\Leftrightarrow & x = \frac{216}{-1485} & & \\\Leftrightarrow & x = \frac{-8}{55} & & \\ & V = \left\{ \frac{-8}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{2})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{25}{2}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-75} & = & \color{red}{-42x} +8 \\\Leftrightarrow & 60x \color{red}{-75} \color{blue}{+75} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{+75} \\\Leftrightarrow & 60x+42x& = & 8+75 \\\Leftrightarrow & \color{red}{102} x& = & 83 \\\Leftrightarrow & x = \frac{83}{102} & & \\ & V = \left\{ \frac{83}{102} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-8} & = & \color{red}{-63x} +5 \\\Leftrightarrow & -144x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +5 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -144x+63x& = & 5+8 \\\Leftrightarrow & \color{red}{-81} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-81} & & \\\Leftrightarrow & x = \frac{-13}{81} & & \\ & V = \left\{ \frac{-13}{81} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-88} & = & \color{red}{693x} +54 \\\Leftrightarrow & -990x \color{red}{-88} \color{blue}{+88} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+88} \\\Leftrightarrow & -990x-693x& = & 54+88 \\\Leftrightarrow & \color{red}{-1683} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-1683} & & \\\Leftrightarrow & x = \frac{-142}{1683} & & \\ & V = \left\{ \frac{-142}{1683} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{+40} & = & \color{red}{-54x} +15 \\\Leftrightarrow & -150x \color{red}{+40} \color{blue}{-40} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{-40} \\\Leftrightarrow & -150x+54x& = & 15-40 \\\Leftrightarrow & \color{red}{-96} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-96} & & \\\Leftrightarrow & x = \frac{25}{96} & & \\ & V = \left\{ \frac{25}{96} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3300}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3300x \color{red}{-180} & = & \color{red}{-770x} +99 \\\Leftrightarrow & 3300x \color{red}{-180} \color{blue}{+180} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{+180} \\\Leftrightarrow & 3300x+770x& = & 99+180 \\\Leftrightarrow & \color{red}{4070} x& = & 279 \\\Leftrightarrow & x = \frac{279}{4070} & & \\ & V = \left\{ \frac{279}{4070} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{35x} +8 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & 84x-35x& = & 8+30 \\\Leftrightarrow & \color{red}{49} x& = & 38 \\\Leftrightarrow & x = \frac{38}{49} & & \\ & V = \left\{ \frac{38}{49} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +44 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 44-54 \\\Leftrightarrow & \color{red}{-1221} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1221} & & \\\Leftrightarrow & x = \frac{10}{1221} & & \\ & V = \left\{ \frac{10}{1221} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{66x} +6 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 693x-66x& = & 6+154 \\\Leftrightarrow & \color{red}{627} x& = & 160 \\\Leftrightarrow & x = \frac{160}{627} & & \\ & V = \left\{ \frac{160}{627} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{441x} +36 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & 504x-441x& = & 36-56 \\\Leftrightarrow & \color{red}{63} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{7})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 15x+\frac{9}{7}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+54} & = & \color{red}{-294x} +49 \\\Leftrightarrow & 630x \color{red}{+54} \color{blue}{-54} \color{blue}{+294x} & = & \color{red}{-294x} +49 \color{blue}{+294x} \color{blue}{-54} \\\Leftrightarrow & 630x+294x& = & 49-54 \\\Leftrightarrow & \color{red}{924} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{924} & & \\ & V = \left\{ \frac{-5}{924} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{-160} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 240x \color{red}{-160} \color{blue}{+160} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+160} \\\Leftrightarrow & 240x+72x& = & 21+160 \\\Leftrightarrow & \color{red}{312} x& = & 181 \\\Leftrightarrow & x = \frac{181}{312} & & \\ & V = \left\{ \frac{181}{312} \right\} & \\\end{align}\)