Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{11})& = & -6x+\frac{5}{3} \\\Leftrightarrow & -28x+\frac{21}{11}& = & -6x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+63} & = & \color{red}{-198x} +55 \\\Leftrightarrow & -924x \color{red}{+63} \color{blue}{-63} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{-63} \\\Leftrightarrow & -924x+198x& = & 55-63 \\\Leftrightarrow & \color{red}{-726} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-726} & & \\\Leftrightarrow & x = \frac{4}{363} & & \\ & V = \left\{ \frac{4}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & 840x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & 840x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{665} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{665} & & \\ & V = \left\{ \frac{-108}{665} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{-490} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-490} & & \\\Leftrightarrow & x = \frac{-67}{245} & & \\ & V = \left\{ \frac{-67}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{16}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+16} & = & \color{red}{-35x} +8 \\\Leftrightarrow & 84x \color{red}{+16} \color{blue}{-16} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-16} \\\Leftrightarrow & 84x+35x& = & 8-16 \\\Leftrightarrow & \color{red}{119} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{119} & & \\ & V = \left\{ \frac{-8}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{3})& = & 6x+\frac{5}{12} \\\Leftrightarrow & -35x-\frac{28}{3}& = & 6x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-112} & = & \color{red}{72x} +5 \\\Leftrightarrow & -420x \color{red}{-112} \color{blue}{+112} \color{blue}{-72x} & = & \color{red}{72x} +5 \color{blue}{-72x} \color{blue}{+112} \\\Leftrightarrow & -420x-72x& = & 5+112 \\\Leftrightarrow & \color{red}{-492} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-492} & & \\\Leftrightarrow & x = \frac{-39}{164} & & \\ & V = \left\{ \frac{-39}{164} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-100} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -240x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & -240x+105x& = & 18+100 \\\Leftrightarrow & \color{red}{-135} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-135} & & \\\Leftrightarrow & x = \frac{-118}{135} & & \\ & V = \left\{ \frac{-118}{135} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{7})& = & -5x+\frac{5}{4} \\\Leftrightarrow & -12x-\frac{18}{7}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{72}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-72} & = & \color{red}{-140x} +35 \\\Leftrightarrow & -336x \color{red}{-72} \color{blue}{+72} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{+72} \\\Leftrightarrow & -336x+140x& = & 35+72 \\\Leftrightarrow & \color{red}{-196} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-196} & & \\\Leftrightarrow & x = \frac{-107}{196} & & \\ & V = \left\{ \frac{-107}{196} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{-132} \\\Leftrightarrow & -825x+220x& = & 30-132 \\\Leftrightarrow & \color{red}{-605} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-605} & & \\\Leftrightarrow & x = \frac{102}{605} & & \\ & V = \left\{ \frac{102}{605} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+330} & = & \color{red}{539x} +14 \\\Leftrightarrow & -2310x \color{red}{+330} \color{blue}{-330} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-330} \\\Leftrightarrow & -2310x-539x& = & 14-330 \\\Leftrightarrow & \color{red}{-2849} x& = & -316 \\\Leftrightarrow & x = \frac{-316}{-2849} & & \\\Leftrightarrow & x = \frac{316}{2849} & & \\ & V = \left\{ \frac{316}{2849} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{20}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{+100} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 875x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & 875x+105x& = & 42-100 \\\Leftrightarrow & \color{red}{980} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{980} & & \\\Leftrightarrow & x = \frac{-29}{490} & & \\ & V = \left\{ \frac{-29}{490} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 14x+\frac{21}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+63} & = & \color{red}{165x} +110 \\\Leftrightarrow & 462x \color{red}{+63} \color{blue}{-63} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-63} \\\Leftrightarrow & 462x-165x& = & 110-63 \\\Leftrightarrow & \color{red}{297} x& = & 47 \\\Leftrightarrow & x = \frac{47}{297} & & \\ & V = \left\{ \frac{47}{297} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -2x+\frac{5}{6} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{378}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 378x \color{red}{-36} & = & \color{red}{-84x} +35 \\\Leftrightarrow & 378x \color{red}{-36} \color{blue}{+36} \color{blue}{+84x} & = & \color{red}{-84x} +35 \color{blue}{+84x} \color{blue}{+36} \\\Leftrightarrow & 378x+84x& = & 35+36 \\\Leftrightarrow & \color{red}{462} x& = & 71 \\\Leftrightarrow & x = \frac{71}{462} & & \\ & V = \left\{ \frac{71}{462} \right\} & \\\end{align}\)