Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{12})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -20x+\frac{25}{12}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{+25} & = & \color{red}{-84x} +28 \\\Leftrightarrow & -240x \color{red}{+25} \color{blue}{-25} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{-25} \\\Leftrightarrow & -240x+84x& = & 28-25 \\\Leftrightarrow & \color{red}{-156} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-156} & & \\\Leftrightarrow & x = \frac{-1}{52} & & \\ & V = \left\{ \frac{-1}{52} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-60} & = & \color{red}{105x} +70 \\\Leftrightarrow & -252x \color{red}{-60} \color{blue}{+60} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+60} \\\Leftrightarrow & -252x-105x& = & 70+60 \\\Leftrightarrow & \color{red}{-357} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-357} & & \\\Leftrightarrow & x = \frac{-130}{357} & & \\ & V = \left\{ \frac{-130}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+231} & = & \color{red}{440x} +16 \\\Leftrightarrow & -2464x \color{red}{+231} \color{blue}{-231} \color{blue}{-440x} & = & \color{red}{440x} +16 \color{blue}{-440x} \color{blue}{-231} \\\Leftrightarrow & -2464x-440x& = & 16-231 \\\Leftrightarrow & \color{red}{-2904} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{-2904} & & \\\Leftrightarrow & x = \frac{215}{2904} & & \\ & V = \left\{ \frac{215}{2904} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & -4x+\frac{9}{4} \\\Leftrightarrow & 9x-\frac{9}{5}& = & -4x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{36}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-80x} +45 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+80x} & = & \color{red}{-80x} +45 \color{blue}{+80x} \color{blue}{+36} \\\Leftrightarrow & 180x+80x& = & 45+36 \\\Leftrightarrow & \color{red}{260} x& = & 81 \\\Leftrightarrow & x = \frac{81}{260} & & \\ & V = \left\{ \frac{81}{260} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{7})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{20}{7}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+20} & = & \color{red}{21x} +10 \\\Leftrightarrow & 56x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & 56x-21x& = & 10-20 \\\Leftrightarrow & \color{red}{35} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{35} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{3})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -10x+\frac{10}{3}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+110} & = & \color{red}{231x} +9 \\\Leftrightarrow & -330x \color{red}{+110} \color{blue}{-110} \color{blue}{-231x} & = & \color{red}{231x} +9 \color{blue}{-231x} \color{blue}{-110} \\\Leftrightarrow & -330x-231x& = & 9-110 \\\Leftrightarrow & \color{red}{-561} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{-561} & & \\\Leftrightarrow & x = \frac{101}{561} & & \\ & V = \left\{ \frac{101}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 20+84 \\\Leftrightarrow & \color{red}{245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{245} & & \\ & V = \left\{ \frac{104}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 8x+\frac{8}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+8} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 40x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & 40x+35x& = & 2-8 \\\Leftrightarrow & \color{red}{75} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{75} & & \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{504}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 504x \color{red}{-48} & = & \color{red}{-112x} +49 \\\Leftrightarrow & 504x \color{red}{-48} \color{blue}{+48} \color{blue}{+112x} & = & \color{red}{-112x} +49 \color{blue}{+112x} \color{blue}{+48} \\\Leftrightarrow & 504x+112x& = & 49+48 \\\Leftrightarrow & \color{red}{616} x& = & 97 \\\Leftrightarrow & x = \frac{97}{616} & & \\ & V = \left\{ \frac{97}{616} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{10})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{9}{10}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{-60}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{-27} & = & \color{red}{-60x} +80 \\\Leftrightarrow & 270x \color{red}{-27} \color{blue}{+27} \color{blue}{+60x} & = & \color{red}{-60x} +80 \color{blue}{+60x} \color{blue}{+27} \\\Leftrightarrow & 270x+60x& = & 80+27 \\\Leftrightarrow & \color{red}{330} x& = & 107 \\\Leftrightarrow & x = \frac{107}{330} & & \\ & V = \left\{ \frac{107}{330} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{2})& = & -8x+\frac{5}{8} \\\Leftrightarrow & 15x-\frac{25}{2}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{100}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-100} & = & \color{red}{-64x} +5 \\\Leftrightarrow & 120x \color{red}{-100} \color{blue}{+100} \color{blue}{+64x} & = & \color{red}{-64x} +5 \color{blue}{+64x} \color{blue}{+100} \\\Leftrightarrow & 120x+64x& = & 5+100 \\\Leftrightarrow & \color{red}{184} x& = & 105 \\\Leftrightarrow & x = \frac{105}{184} & & \\ & V = \left\{ \frac{105}{184} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{8})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{-147} & = & \color{red}{224x} +80 \\\Leftrightarrow & -1960x \color{red}{-147} \color{blue}{+147} \color{blue}{-224x} & = & \color{red}{224x} +80 \color{blue}{-224x} \color{blue}{+147} \\\Leftrightarrow & -1960x-224x& = & 80+147 \\\Leftrightarrow & \color{red}{-2184} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-2184} & & \\\Leftrightarrow & x = \frac{-227}{2184} & & \\ & V = \left\{ \frac{-227}{2184} \right\} & \\\end{align}\)