Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{8})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -9x+\frac{9}{8}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-360}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -360x \color{red}{+45} & = & \color{red}{-200x} +56 \\\Leftrightarrow & -360x \color{red}{+45} \color{blue}{-45} \color{blue}{+200x} & = & \color{red}{-200x} +56 \color{blue}{+200x} \color{blue}{-45} \\\Leftrightarrow & -360x+200x& = & 56-45 \\\Leftrightarrow & \color{red}{-160} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-160} & & \\\Leftrightarrow & x = \frac{-11}{160} & & \\ & V = \left\{ \frac{-11}{160} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 14x-\frac{35}{2}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{315}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-315} & = & \color{red}{-90x} +16 \\\Leftrightarrow & 252x \color{red}{-315} \color{blue}{+315} \color{blue}{+90x} & = & \color{red}{-90x} +16 \color{blue}{+90x} \color{blue}{+315} \\\Leftrightarrow & 252x+90x& = & 16+315 \\\Leftrightarrow & \color{red}{342} x& = & 331 \\\Leftrightarrow & x = \frac{331}{342} & & \\ & V = \left\{ \frac{331}{342} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{-108x} +27 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{-80} \\\Leftrightarrow & -720x+108x& = & 27-80 \\\Leftrightarrow & \color{red}{-612} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-612} & & \\\Leftrightarrow & x = \frac{53}{612} & & \\ & V = \left\{ \frac{53}{612} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -8x+\frac{5}{4} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -8x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-80} & = & \color{red}{-224x} +35 \\\Leftrightarrow & 700x \color{red}{-80} \color{blue}{+80} \color{blue}{+224x} & = & \color{red}{-224x} +35 \color{blue}{+224x} \color{blue}{+80} \\\Leftrightarrow & 700x+224x& = & 35+80 \\\Leftrightarrow & \color{red}{924} x& = & 115 \\\Leftrightarrow & x = \frac{115}{924} & & \\ & V = \left\{ \frac{115}{924} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{10})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{9}{10}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-9} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 120x \color{red}{-9} \color{blue}{+9} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+9} \\\Leftrightarrow & 120x+70x& = & 45+9 \\\Leftrightarrow & \color{red}{190} x& = & 54 \\\Leftrightarrow & x = \frac{54}{190} & & \\\Leftrightarrow & x = \frac{27}{95} & & \\ & V = \left\{ \frac{27}{95} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+72} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -360x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -360x+75x& = & 40-72 \\\Leftrightarrow & \color{red}{-285} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-285} & & \\\Leftrightarrow & x = \frac{32}{285} & & \\ & V = \left\{ \frac{32}{285} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{-63} & = & \color{red}{192x} +16 \\\Leftrightarrow & -504x \color{red}{-63} \color{blue}{+63} \color{blue}{-192x} & = & \color{red}{192x} +16 \color{blue}{-192x} \color{blue}{+63} \\\Leftrightarrow & -504x-192x& = & 16+63 \\\Leftrightarrow & \color{red}{-696} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-696} & & \\\Leftrightarrow & x = \frac{-79}{696} & & \\ & V = \left\{ \frac{-79}{696} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 18x-\frac{12}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-84} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 1386x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & 1386x+385x& = & 44+84 \\\Leftrightarrow & \color{red}{1771} x& = & 128 \\\Leftrightarrow & x = \frac{128}{1771} & & \\ & V = \left\{ \frac{128}{1771} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{11})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 14x-\frac{35}{11}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-245} & = & \color{red}{231x} +99 \\\Leftrightarrow & 1078x \color{red}{-245} \color{blue}{+245} \color{blue}{-231x} & = & \color{red}{231x} +99 \color{blue}{-231x} \color{blue}{+245} \\\Leftrightarrow & 1078x-231x& = & 99+245 \\\Leftrightarrow & \color{red}{847} x& = & 344 \\\Leftrightarrow & x = \frac{344}{847} & & \\ & V = \left\{ \frac{344}{847} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{245x} +15 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{-245x} & = & \color{red}{245x} +15 \color{blue}{-245x} \color{blue}{-28} \\\Leftrightarrow & 350x-245x& = & 15-28 \\\Leftrightarrow & \color{red}{105} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{105} & & \\ & V = \left\{ \frac{-13}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +40 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 40-84 \\\Leftrightarrow & \color{red}{-595} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-595} & & \\\Leftrightarrow & x = \frac{44}{595} & & \\ & V = \left\{ \frac{44}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{6})& = & 4x+\frac{3}{8} \\\Leftrightarrow & -15x+\frac{25}{6}& = & 4x+\frac{3}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x+ \frac{100}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{+100} & = & \color{red}{96x} +9 \\\Leftrightarrow & -360x \color{red}{+100} \color{blue}{-100} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{-100} \\\Leftrightarrow & -360x-96x& = & 9-100 \\\Leftrightarrow & \color{red}{-456} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{-456} & & \\\Leftrightarrow & x = \frac{91}{456} & & \\ & V = \left\{ \frac{91}{456} \right\} & \\\end{align}\)