Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-140} & = & \color{red}{-63x} +24 \\\Leftrightarrow & -525x \color{red}{-140} \color{blue}{+140} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{+140} \\\Leftrightarrow & -525x+63x& = & 24+140 \\\Leftrightarrow & \color{red}{-462} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-462} & & \\\Leftrightarrow & x = \frac{-82}{231} & & \\ & V = \left\{ \frac{-82}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{6})& = & -8x+\frac{7}{9} \\\Leftrightarrow & -21x-\frac{35}{6}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-378}{ \color{blue}{18} }x- \frac{105}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -378x \color{red}{-105} & = & \color{red}{-144x} +14 \\\Leftrightarrow & -378x \color{red}{-105} \color{blue}{+105} \color{blue}{+144x} & = & \color{red}{-144x} +14 \color{blue}{+144x} \color{blue}{+105} \\\Leftrightarrow & -378x+144x& = & 14+105 \\\Leftrightarrow & \color{red}{-234} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-234} & & \\\Leftrightarrow & x = \frac{-119}{234} & & \\ & V = \left\{ \frac{-119}{234} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1200}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1200x \color{red}{+144} & = & \color{red}{180x} +35 \\\Leftrightarrow & 1200x \color{red}{+144} \color{blue}{-144} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{-144} \\\Leftrightarrow & 1200x-180x& = & 35-144 \\\Leftrightarrow & \color{red}{1020} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1020} & & \\ & V = \left\{ \frac{-109}{1020} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 6x+\frac{9}{10}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+9} & = & \color{red}{70x} +14 \\\Leftrightarrow & 60x \color{red}{+9} \color{blue}{-9} \color{blue}{-70x} & = & \color{red}{70x} +14 \color{blue}{-70x} \color{blue}{-9} \\\Leftrightarrow & 60x-70x& = & 14-9 \\\Leftrightarrow & \color{red}{-10} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-10} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{-45x} +10 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-36} \\\Leftrightarrow & -120x+45x& = & 10-36 \\\Leftrightarrow & \color{red}{-75} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-75} & & \\\Leftrightarrow & x = \frac{26}{75} & & \\ & V = \left\{ \frac{26}{75} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{+50} \\\Leftrightarrow & 350x+105x& = & 42+50 \\\Leftrightarrow & \color{red}{455} x& = & 92 \\\Leftrightarrow & x = \frac{92}{455} & & \\ & V = \left\{ \frac{92}{455} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+110} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -462x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & -462x+539x& = & 35-110 \\\Leftrightarrow & \color{red}{77} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{77} & & \\ & V = \left\{ \frac{-75}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-36} & = & \color{red}{165x} +44 \\\Leftrightarrow & -396x \color{red}{-36} \color{blue}{+36} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+36} \\\Leftrightarrow & -396x-165x& = & 44+36 \\\Leftrightarrow & \color{red}{-561} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-561} & & \\\Leftrightarrow & x = \frac{-80}{561} & & \\ & V = \left\{ \frac{-80}{561} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{4}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+36} & = & \color{red}{-441x} +70 \\\Leftrightarrow & -378x \color{red}{+36} \color{blue}{-36} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-36} \\\Leftrightarrow & -378x+441x& = & 70-36 \\\Leftrightarrow & \color{red}{63} x& = & 34 \\\Leftrightarrow & x = \frac{34}{63} & & \\ & V = \left\{ \frac{34}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 28x+\frac{28}{3}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+84} & = & \color{red}{81x} +4 \\\Leftrightarrow & 252x \color{red}{+84} \color{blue}{-84} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{-84} \\\Leftrightarrow & 252x-81x& = & 4-84 \\\Leftrightarrow & \color{red}{171} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{171} & & \\ & V = \left\{ \frac{-80}{171} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{6})& = & -8x+\frac{7}{5} \\\Leftrightarrow & 25x-\frac{25}{6}& = & -8x+\frac{7}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{750}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{42}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 750x \color{red}{-125} & = & \color{red}{-240x} +42 \\\Leftrightarrow & 750x \color{red}{-125} \color{blue}{+125} \color{blue}{+240x} & = & \color{red}{-240x} +42 \color{blue}{+240x} \color{blue}{+125} \\\Leftrightarrow & 750x+240x& = & 42+125 \\\Leftrightarrow & \color{red}{990} x& = & 167 \\\Leftrightarrow & x = \frac{167}{990} & & \\ & V = \left\{ \frac{167}{990} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-400}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{-280x} +48 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{+280x} & = & \color{red}{-280x} +48 \color{blue}{+280x} \color{blue}{+75} \\\Leftrightarrow & -400x+280x& = & 48+75 \\\Leftrightarrow & \color{red}{-120} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-120} & & \\\Leftrightarrow & x = \frac{-41}{40} & & \\ & V = \left\{ \frac{-41}{40} \right\} & \\\end{align}\)