Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{5})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 9x+\frac{9}{5}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+18} & = & \color{red}{20x} +45 \\\Leftrightarrow & 90x \color{red}{+18} \color{blue}{-18} \color{blue}{-20x} & = & \color{red}{20x} +45 \color{blue}{-20x} \color{blue}{-18} \\\Leftrightarrow & 90x-20x& = & 45-18 \\\Leftrightarrow & \color{red}{70} x& = & 27 \\\Leftrightarrow & x = \frac{27}{70} & & \\ & V = \left\{ \frac{27}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-88} & = & \color{red}{-165x} +30 \\\Leftrightarrow & 198x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +30 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 198x+165x& = & 30+88 \\\Leftrightarrow & \color{red}{363} x& = & 118 \\\Leftrightarrow & x = \frac{118}{363} & & \\ & V = \left\{ \frac{118}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+12} \\\Leftrightarrow & -84x+98x& = & 21+12 \\\Leftrightarrow & \color{red}{14} x& = & 33 \\\Leftrightarrow & x = \frac{33}{14} & & \\ & V = \left\{ \frac{33}{14} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{9})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{20}{9}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+40} & = & \color{red}{162x} +27 \\\Leftrightarrow & 144x \color{red}{+40} \color{blue}{-40} \color{blue}{-162x} & = & \color{red}{162x} +27 \color{blue}{-162x} \color{blue}{-40} \\\Leftrightarrow & 144x-162x& = & 27-40 \\\Leftrightarrow & \color{red}{-18} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-18} & & \\\Leftrightarrow & x = \frac{13}{18} & & \\ & V = \left\{ \frac{13}{18} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{2})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -35x-\frac{35}{2}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-70}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-6}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -70x \color{red}{-35} & = & \color{red}{-6x} +5 \\\Leftrightarrow & -70x \color{red}{-35} \color{blue}{+35} \color{blue}{+6x} & = & \color{red}{-6x} +5 \color{blue}{+6x} \color{blue}{+35} \\\Leftrightarrow & -70x+6x& = & 5+35 \\\Leftrightarrow & \color{red}{-64} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-64} & & \\\Leftrightarrow & x = \frac{-5}{8} & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{2})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{15}{2}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-165} & = & \color{red}{-154x} +12 \\\Leftrightarrow & 330x \color{red}{-165} \color{blue}{+165} \color{blue}{+154x} & = & \color{red}{-154x} +12 \color{blue}{+154x} \color{blue}{+165} \\\Leftrightarrow & 330x+154x& = & 12+165 \\\Leftrightarrow & \color{red}{484} x& = & 177 \\\Leftrightarrow & x = \frac{177}{484} & & \\ & V = \left\{ \frac{177}{484} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+198} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 1320x \color{red}{+198} \color{blue}{-198} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-198} \\\Leftrightarrow & 1320x+275x& = & 20-198 \\\Leftrightarrow & \color{red}{1595} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{1595} & & \\ & V = \left\{ \frac{-178}{1595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & -120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1320}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{30}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1320x \color{red}{-275} & = & \color{red}{594x} +30 \\\Leftrightarrow & 1320x \color{red}{-275} \color{blue}{+275} \color{blue}{-594x} & = & \color{red}{594x} +30 \color{blue}{-594x} \color{blue}{+275} \\\Leftrightarrow & 1320x-594x& = & 30+275 \\\Leftrightarrow & \color{red}{726} x& = & 305 \\\Leftrightarrow & x = \frac{305}{726} & & \\ & V = \left\{ \frac{305}{726} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+150} & = & \color{red}{175x} +56 \\\Leftrightarrow & -840x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -840x-175x& = & 56-150 \\\Leftrightarrow & \color{red}{-1015} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-1015} & & \\\Leftrightarrow & x = \frac{94}{1015} & & \\ & V = \left\{ \frac{94}{1015} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{11})& = & -6x+\frac{8}{7} \\\Leftrightarrow & -28x+\frac{28}{11}& = & -6x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2156}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2156x \color{red}{+196} & = & \color{red}{-462x} +88 \\\Leftrightarrow & -2156x \color{red}{+196} \color{blue}{-196} \color{blue}{+462x} & = & \color{red}{-462x} +88 \color{blue}{+462x} \color{blue}{-196} \\\Leftrightarrow & -2156x+462x& = & 88-196 \\\Leftrightarrow & \color{red}{-1694} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-1694} & & \\\Leftrightarrow & x = \frac{54}{847} & & \\ & V = \left\{ \frac{54}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -3x+\frac{3}{5} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{-45x} +9 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{+45x} & = & \color{red}{-45x} +9 \color{blue}{+45x} \color{blue}{+70} \\\Leftrightarrow & 420x+45x& = & 9+70 \\\Leftrightarrow & \color{red}{465} x& = & 79 \\\Leftrightarrow & x = \frac{79}{465} & & \\ & V = \left\{ \frac{79}{465} \right\} & \\\end{align}\)