Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{7})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{8}{7}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-24} & = & \color{red}{-63x} +28 \\\Leftrightarrow & 420x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +28 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & 420x+63x& = & 28+24 \\\Leftrightarrow & \color{red}{483} x& = & 52 \\\Leftrightarrow & x = \frac{52}{483} & & \\ & V = \left\{ \frac{52}{483} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +3 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 3+10 \\\Leftrightarrow & \color{red}{-119} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-119} & & \\\Leftrightarrow & x = \frac{-13}{119} & & \\ & V = \left\{ \frac{-13}{119} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 35+66 \\\Leftrightarrow & \color{red}{77} x& = & 101 \\\Leftrightarrow & x = \frac{101}{77} & & \\ & V = \left\{ \frac{101}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & -924x+385x& = & 22+84 \\\Leftrightarrow & \color{red}{-539} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-539} & & \\\Leftrightarrow & x = \frac{-106}{539} & & \\ & V = \left\{ \frac{-106}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +2 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 2-12 \\\Leftrightarrow & \color{red}{55} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{55} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-224}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -224x \color{red}{-32} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -224x \color{red}{-32} \color{blue}{+32} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+32} \\\Leftrightarrow & -224x+98x& = & 21+32 \\\Leftrightarrow & \color{red}{-126} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-126} & & \\\Leftrightarrow & x = \frac{-53}{126} & & \\ & V = \left\{ \frac{-53}{126} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{9})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 10x-\frac{25}{9}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x- \frac{100}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{45}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{-100} & = & \color{red}{-252x} +45 \\\Leftrightarrow & 360x \color{red}{-100} \color{blue}{+100} \color{blue}{+252x} & = & \color{red}{-252x} +45 \color{blue}{+252x} \color{blue}{+100} \\\Leftrightarrow & 360x+252x& = & 45+100 \\\Leftrightarrow & \color{red}{612} x& = & 145 \\\Leftrightarrow & x = \frac{145}{612} & & \\ & V = \left\{ \frac{145}{612} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{4}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{4}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-4} & = & \color{red}{33x} +4 \\\Leftrightarrow & -88x \color{red}{-4} \color{blue}{+4} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{+4} \\\Leftrightarrow & -88x-33x& = & 4+4 \\\Leftrightarrow & \color{red}{-121} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-121} & & \\\Leftrightarrow & x = \frac{-8}{121} & & \\ & V = \left\{ \frac{-8}{121} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{36x} +15 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{-36x} & = & \color{red}{36x} +15 \color{blue}{-36x} \color{blue}{+56} \\\Leftrightarrow & 168x-36x& = & 15+56 \\\Leftrightarrow & \color{red}{132} x& = & 71 \\\Leftrightarrow & x = \frac{71}{132} & & \\ & V = \left\{ \frac{71}{132} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{-60} & = & \color{red}{350x} +21 \\\Leftrightarrow & -630x \color{red}{-60} \color{blue}{+60} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{+60} \\\Leftrightarrow & -630x-350x& = & 21+60 \\\Leftrightarrow & \color{red}{-980} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-980} & & \\\Leftrightarrow & x = \frac{-81}{980} & & \\ & V = \left\{ \frac{-81}{980} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -20x+\frac{10}{3}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+10} & = & \color{red}{21x} +5 \\\Leftrightarrow & -60x \color{red}{+10} \color{blue}{-10} \color{blue}{-21x} & = & \color{red}{21x} +5 \color{blue}{-21x} \color{blue}{-10} \\\Leftrightarrow & -60x-21x& = & 5-10 \\\Leftrightarrow & \color{red}{-81} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-81} & & \\\Leftrightarrow & x = \frac{5}{81} & & \\ & V = \left\{ \frac{5}{81} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{8}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-16} & = & \color{red}{-110x} +99 \\\Leftrightarrow & -264x \color{red}{-16} \color{blue}{+16} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+16} \\\Leftrightarrow & -264x+110x& = & 99+16 \\\Leftrightarrow & \color{red}{-154} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-154} & & \\\Leftrightarrow & x = \frac{-115}{154} & & \\ & V = \left\{ \frac{-115}{154} \right\} & \\\end{align}\)