Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{8}{9}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{-135x} +54 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{+135x} & = & \color{red}{-135x} +54 \color{blue}{+135x} \color{blue}{+40} \\\Leftrightarrow & 180x+135x& = & 54+40 \\\Leftrightarrow & \color{red}{315} x& = & 94 \\\Leftrightarrow & x = \frac{94}{315} & & \\ & V = \left\{ \frac{94}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 1320x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 1320x+275x& = & 30-132 \\\Leftrightarrow & \color{red}{1595} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{1595} & & \\ & V = \left\{ \frac{-102}{1595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{3})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{25}{3}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{50}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{+50} \\\Leftrightarrow & 120x+42x& = & 21+50 \\\Leftrightarrow & \color{red}{162} x& = & 71 \\\Leftrightarrow & x = \frac{71}{162} & & \\ & V = \left\{ \frac{71}{162} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{-25x} +2 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & -60x+25x& = & 2+12 \\\Leftrightarrow & \color{red}{-35} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-35} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{6})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -10x-\frac{25}{6}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-660}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{24}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -660x \color{red}{-275} & = & \color{red}{-462x} +24 \\\Leftrightarrow & -660x \color{red}{-275} \color{blue}{+275} \color{blue}{+462x} & = & \color{red}{-462x} +24 \color{blue}{+462x} \color{blue}{+275} \\\Leftrightarrow & -660x+462x& = & 24+275 \\\Leftrightarrow & \color{red}{-198} x& = & 299 \\\Leftrightarrow & x = \frac{299}{-198} & & \\\Leftrightarrow & x = \frac{-299}{198} & & \\ & V = \left\{ \frac{-299}{198} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{7})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 25x-\frac{10}{7}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{-80} & = & \color{red}{-112x} +49 \\\Leftrightarrow & 1400x \color{red}{-80} \color{blue}{+80} \color{blue}{+112x} & = & \color{red}{-112x} +49 \color{blue}{+112x} \color{blue}{+80} \\\Leftrightarrow & 1400x+112x& = & 49+80 \\\Leftrightarrow & \color{red}{1512} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1512} & & \\\Leftrightarrow & x = \frac{43}{504} & & \\ & V = \left\{ \frac{43}{504} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+10} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -42x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -42x+49x& = & 9-10 \\\Leftrightarrow & \color{red}{7} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{4}{9}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{162x} +15 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-162x} & = & \color{red}{162x} +15 \color{blue}{-162x} \color{blue}{-8} \\\Leftrightarrow & 180x-162x& = & 15-8 \\\Leftrightarrow & \color{red}{18} x& = & 7 \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{154x} +55 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+36} \\\Leftrightarrow & 660x-154x& = & 55+36 \\\Leftrightarrow & \color{red}{506} x& = & 91 \\\Leftrightarrow & x = \frac{91}{506} & & \\ & V = \left\{ \frac{91}{506} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-40} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 140x \color{red}{-40} \color{blue}{+40} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+40} \\\Leftrightarrow & 140x+98x& = & 49+40 \\\Leftrightarrow & \color{red}{238} x& = & 89 \\\Leftrightarrow & x = \frac{89}{238} & & \\ & V = \left\{ \frac{89}{238} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{2})& = & 6x+\frac{4}{9} \\\Leftrightarrow & -25x+\frac{25}{2}& = & 6x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{108}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+225} & = & \color{red}{108x} +8 \\\Leftrightarrow & -450x \color{red}{+225} \color{blue}{-225} \color{blue}{-108x} & = & \color{red}{108x} +8 \color{blue}{-108x} \color{blue}{-225} \\\Leftrightarrow & -450x-108x& = & 8-225 \\\Leftrightarrow & \color{red}{-558} x& = & -217 \\\Leftrightarrow & x = \frac{-217}{-558} & & \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+140} & = & \color{red}{120x} +24 \\\Leftrightarrow & -315x \color{red}{+140} \color{blue}{-140} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{-140} \\\Leftrightarrow & -315x-120x& = & 24-140 \\\Leftrightarrow & \color{red}{-435} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{-435} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)