Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -2x+\frac{8}{5} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -2x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{-105} & = & \color{red}{-80x} +64 \\\Leftrightarrow & -1120x \color{red}{-105} \color{blue}{+105} \color{blue}{+80x} & = & \color{red}{-80x} +64 \color{blue}{+80x} \color{blue}{+105} \\\Leftrightarrow & -1120x+80x& = & 64+105 \\\Leftrightarrow & \color{red}{-1040} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-1040} & & \\\Leftrightarrow & x = \frac{-13}{80} & & \\ & V = \left\{ \frac{-13}{80} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{4})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{15}{4}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{+165} & = & \color{red}{88x} +32 \\\Leftrightarrow & 396x \color{red}{+165} \color{blue}{-165} \color{blue}{-88x} & = & \color{red}{88x} +32 \color{blue}{-88x} \color{blue}{-165} \\\Leftrightarrow & 396x-88x& = & 32-165 \\\Leftrightarrow & \color{red}{308} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{308} & & \\\Leftrightarrow & x = \frac{-19}{44} & & \\ & V = \left\{ \frac{-19}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-112} & = & \color{red}{539x} +44 \\\Leftrightarrow & -1540x \color{red}{-112} \color{blue}{+112} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+112} \\\Leftrightarrow & -1540x-539x& = & 44+112 \\\Leftrightarrow & \color{red}{-2079} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-2079} & & \\\Leftrightarrow & x = \frac{-52}{693} & & \\ & V = \left\{ \frac{-52}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{231x} +44 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 792x-231x& = & 44+54 \\\Leftrightarrow & \color{red}{561} x& = & 98 \\\Leftrightarrow & x = \frac{98}{561} & & \\ & V = \left\{ \frac{98}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-10} & = & \color{red}{35x} +2 \\\Leftrightarrow & 56x \color{red}{-10} \color{blue}{+10} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+10} \\\Leftrightarrow & 56x-35x& = & 2+10 \\\Leftrightarrow & \color{red}{21} x& = & 12 \\\Leftrightarrow & x = \frac{12}{21} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & 8x+\frac{9}{5} \\\Leftrightarrow & 21x-\frac{14}{5}& = & 8x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{105}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{40x} +9 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{+14} \\\Leftrightarrow & 105x-40x& = & 9+14 \\\Leftrightarrow & \color{red}{65} x& = & 23 \\\Leftrightarrow & x = \frac{23}{65} & & \\ & V = \left\{ \frac{23}{65} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{56x} +7 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{-21} \\\Leftrightarrow & -224x-56x& = & 7-21 \\\Leftrightarrow & \color{red}{-280} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-280} & & \\\Leftrightarrow & x = \frac{1}{20} & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 270x+75x& = & 20+36 \\\Leftrightarrow & \color{red}{345} x& = & 56 \\\Leftrightarrow & x = \frac{56}{345} & & \\ & V = \left\{ \frac{56}{345} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{3})& = & -8x+\frac{7}{4} \\\Leftrightarrow & -21x+\frac{35}{3}& = & -8x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+140} & = & \color{red}{-96x} +21 \\\Leftrightarrow & -252x \color{red}{+140} \color{blue}{-140} \color{blue}{+96x} & = & \color{red}{-96x} +21 \color{blue}{+96x} \color{blue}{-140} \\\Leftrightarrow & -252x+96x& = & 21-140 \\\Leftrightarrow & \color{red}{-156} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-156} & & \\\Leftrightarrow & x = \frac{119}{156} & & \\ & V = \left\{ \frac{119}{156} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{9}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{27}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-27} & = & \color{red}{165x} +22 \\\Leftrightarrow & 198x \color{red}{-27} \color{blue}{+27} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+27} \\\Leftrightarrow & 198x-165x& = & 22+27 \\\Leftrightarrow & \color{red}{33} x& = & 49 \\\Leftrightarrow & x = \frac{49}{33} & & \\ & V = \left\{ \frac{49}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{3})& = & -8x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{20}{3}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{-48x} +5 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{+48x} & = & \color{red}{-48x} +5 \color{blue}{+48x} \color{blue}{-40} \\\Leftrightarrow & -90x+48x& = & 5-40 \\\Leftrightarrow & \color{red}{-42} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-42} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{11})& = & -3x+\frac{9}{11} \\\Leftrightarrow & 8x+\frac{6}{11}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+6} & = & \color{red}{-33x} +9 \\\Leftrightarrow & 88x \color{red}{+6} \color{blue}{-6} \color{blue}{+33x} & = & \color{red}{-33x} +9 \color{blue}{+33x} \color{blue}{-6} \\\Leftrightarrow & 88x+33x& = & 9-6 \\\Leftrightarrow & \color{red}{121} x& = & 3 \\\Leftrightarrow & x = \frac{3}{121} & & \\ & V = \left\{ \frac{3}{121} \right\} & \\\end{align}\)