Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{-40} & = & \color{red}{-126x} +63 \\\Leftrightarrow & -288x \color{red}{-40} \color{blue}{+40} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{+40} \\\Leftrightarrow & -288x+126x& = & 63+40 \\\Leftrightarrow & \color{red}{-162} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-162} & & \\\Leftrightarrow & x = \frac{-103}{162} & & \\ & V = \left\{ \frac{-103}{162} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-16} & = & \color{red}{-54x} +9 \\\Leftrightarrow & -48x \color{red}{-16} \color{blue}{+16} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{+16} \\\Leftrightarrow & -48x+54x& = & 9+16 \\\Leftrightarrow & \color{red}{6} x& = & 25 \\\Leftrightarrow & x = \frac{25}{6} & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{3})& = & 4x+\frac{3}{10} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+200} & = & \color{red}{120x} +9 \\\Leftrightarrow & -450x \color{red}{+200} \color{blue}{-200} \color{blue}{-120x} & = & \color{red}{120x} +9 \color{blue}{-120x} \color{blue}{-200} \\\Leftrightarrow & -450x-120x& = & 9-200 \\\Leftrightarrow & \color{red}{-570} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-570} & & \\\Leftrightarrow & x = \frac{191}{570} & & \\ & V = \left\{ \frac{191}{570} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-16} & = & \color{red}{-18x} +5 \\\Leftrightarrow & -48x \color{red}{-16} \color{blue}{+16} \color{blue}{+18x} & = & \color{red}{-18x} +5 \color{blue}{+18x} \color{blue}{+16} \\\Leftrightarrow & -48x+18x& = & 5+16 \\\Leftrightarrow & \color{red}{-30} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-30} & & \\\Leftrightarrow & x = \frac{-7}{10} & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 16x+\frac{16}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+112} & = & \color{red}{-539x} +99 \\\Leftrightarrow & 1232x \color{red}{+112} \color{blue}{-112} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{-112} \\\Leftrightarrow & 1232x+539x& = & 99-112 \\\Leftrightarrow & \color{red}{1771} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{1771} & & \\ & V = \left\{ \frac{-13}{1771} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-275x} +40 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +40 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 660x+275x& = & 40+132 \\\Leftrightarrow & \color{red}{935} x& = & 172 \\\Leftrightarrow & x = \frac{172}{935} & & \\ & V = \left\{ \frac{172}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{9})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{20}{9}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-900}{ \color{blue}{90} }x+ \frac{200}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -900x \color{red}{+200} & = & \color{red}{-630x} +81 \\\Leftrightarrow & -900x \color{red}{+200} \color{blue}{-200} \color{blue}{+630x} & = & \color{red}{-630x} +81 \color{blue}{+630x} \color{blue}{-200} \\\Leftrightarrow & -900x+630x& = & 81-200 \\\Leftrightarrow & \color{red}{-270} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-270} & & \\\Leftrightarrow & x = \frac{119}{270} & & \\ & V = \left\{ \frac{119}{270} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{3}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{-80x} +12 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{+80x} & = & \color{red}{-80x} +12 \color{blue}{+80x} \color{blue}{-75} \\\Leftrightarrow & -300x+80x& = & 12-75 \\\Leftrightarrow & \color{red}{-220} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-220} & & \\\Leftrightarrow & x = \frac{63}{220} & & \\ & V = \left\{ \frac{63}{220} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{3})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{-80} & = & \color{red}{60x} +15 \\\Leftrightarrow & -300x \color{red}{-80} \color{blue}{+80} \color{blue}{-60x} & = & \color{red}{60x} +15 \color{blue}{-60x} \color{blue}{+80} \\\Leftrightarrow & -300x-60x& = & 15+80 \\\Leftrightarrow & \color{red}{-360} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-360} & & \\\Leftrightarrow & x = \frac{-19}{72} & & \\ & V = \left\{ \frac{-19}{72} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{15}{2}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{+45} & = & \color{red}{-42x} +16 \\\Leftrightarrow & 72x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +16 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & 72x+42x& = & 16-45 \\\Leftrightarrow & \color{red}{114} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{114} & & \\ & V = \left\{ \frac{-29}{114} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -8x+\frac{3}{8} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{504}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 504x \color{red}{+48} & = & \color{red}{-448x} +21 \\\Leftrightarrow & 504x \color{red}{+48} \color{blue}{-48} \color{blue}{+448x} & = & \color{red}{-448x} +21 \color{blue}{+448x} \color{blue}{-48} \\\Leftrightarrow & 504x+448x& = & 21-48 \\\Leftrightarrow & \color{red}{952} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{952} & & \\ & V = \left\{ \frac{-27}{952} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{4})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{28}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{140x} +28 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +28 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 300x-140x& = & 28+75 \\\Leftrightarrow & \color{red}{160} x& = & 103 \\\Leftrightarrow & x = \frac{103}{160} & & \\ & V = \left\{ \frac{103}{160} \right\} & \\\end{align}\)