Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{275x} +40 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 495x-275x& = & 40+132 \\\Leftrightarrow & \color{red}{220} x& = & 172 \\\Leftrightarrow & x = \frac{172}{220} & & \\\Leftrightarrow & x = \frac{43}{55} & & \\ & V = \left\{ \frac{43}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+45} & = & \color{red}{48x} +8 \\\Leftrightarrow & -90x \color{red}{+45} \color{blue}{-45} \color{blue}{-48x} & = & \color{red}{48x} +8 \color{blue}{-48x} \color{blue}{-45} \\\Leftrightarrow & -90x-48x& = & 8-45 \\\Leftrightarrow & \color{red}{-138} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-138} & & \\\Leftrightarrow & x = \frac{37}{138} & & \\ & V = \left\{ \frac{37}{138} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{3})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -8x+\frac{4}{3}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+8} & = & \color{red}{-54x} +5 \\\Leftrightarrow & -48x \color{red}{+8} \color{blue}{-8} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-8} \\\Leftrightarrow & -48x+54x& = & 5-8 \\\Leftrightarrow & \color{red}{6} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{6} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{480}{ \color{blue}{60} }x- \frac{48}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 480x \color{red}{-48} & = & \color{red}{-420x} +25 \\\Leftrightarrow & 480x \color{red}{-48} \color{blue}{+48} \color{blue}{+420x} & = & \color{red}{-420x} +25 \color{blue}{+420x} \color{blue}{+48} \\\Leftrightarrow & 480x+420x& = & 25+48 \\\Leftrightarrow & \color{red}{900} x& = & 73 \\\Leftrightarrow & x = \frac{73}{900} & & \\ & V = \left\{ \frac{73}{900} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{+45} & = & \color{red}{120x} +20 \\\Leftrightarrow & 216x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +20 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & 216x-120x& = & 20-45 \\\Leftrightarrow & \color{red}{96} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{96} & & \\ & V = \left\{ \frac{-25}{96} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{8})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 9x+\frac{9}{8}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+9} & = & \color{red}{40x} +14 \\\Leftrightarrow & 72x \color{red}{+9} \color{blue}{-9} \color{blue}{-40x} & = & \color{red}{40x} +14 \color{blue}{-40x} \color{blue}{-9} \\\Leftrightarrow & 72x-40x& = & 14-9 \\\Leftrightarrow & \color{red}{32} x& = & 5 \\\Leftrightarrow & x = \frac{5}{32} & & \\ & V = \left\{ \frac{5}{32} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1980}{ \color{blue}{66} }x- \frac{180}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{462x} +55 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-462x} & = & \color{red}{462x} +55 \color{blue}{-462x} \color{blue}{+180} \\\Leftrightarrow & -1980x-462x& = & 55+180 \\\Leftrightarrow & \color{red}{-2442} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-2442} & & \\\Leftrightarrow & x = \frac{-235}{2442} & & \\ & V = \left\{ \frac{-235}{2442} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -4x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-6} & = & \color{red}{-28x} +9 \\\Leftrightarrow & -105x \color{red}{-6} \color{blue}{+6} \color{blue}{+28x} & = & \color{red}{-28x} +9 \color{blue}{+28x} \color{blue}{+6} \\\Leftrightarrow & -105x+28x& = & 9+6 \\\Leftrightarrow & \color{red}{-77} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-77} & & \\\Leftrightarrow & x = \frac{-15}{77} & & \\ & V = \left\{ \frac{-15}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{10})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-9} \\\Leftrightarrow & -60x+70x& = & 45-9 \\\Leftrightarrow & \color{red}{10} x& = & 36 \\\Leftrightarrow & x = \frac{36}{10} & & \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 21x-\frac{35}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{315}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-315} & = & \color{red}{-495x} +110 \\\Leftrightarrow & 2079x \color{red}{-315} \color{blue}{+315} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{+315} \\\Leftrightarrow & 2079x+495x& = & 110+315 \\\Leftrightarrow & \color{red}{2574} x& = & 425 \\\Leftrightarrow & x = \frac{425}{2574} & & \\ & V = \left\{ \frac{425}{2574} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{5}{9} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{5}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-576}{ \color{blue}{72} }x+ \frac{40}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-189} & = & \color{red}{-576x} +40 \\\Leftrightarrow & -1512x \color{red}{-189} \color{blue}{+189} \color{blue}{+576x} & = & \color{red}{-576x} +40 \color{blue}{+576x} \color{blue}{+189} \\\Leftrightarrow & -1512x+576x& = & 40+189 \\\Leftrightarrow & \color{red}{-936} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-936} & & \\\Leftrightarrow & x = \frac{-229}{936} & & \\ & V = \left\{ \frac{-229}{936} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+63} & = & \color{red}{72x} +80 \\\Leftrightarrow & 672x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +80 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & 672x-72x& = & 80-63 \\\Leftrightarrow & \color{red}{600} x& = & 17 \\\Leftrightarrow & x = \frac{17}{600} & & \\ & V = \left\{ \frac{17}{600} \right\} & \\\end{align}\)