Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 18x+\frac{24}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x+ \frac{216}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{+216} & = & \color{red}{315x} +56 \\\Leftrightarrow & 1134x \color{red}{+216} \color{blue}{-216} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-216} \\\Leftrightarrow & 1134x-315x& = & 56-216 \\\Leftrightarrow & \color{red}{819} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{819} & & \\ & V = \left\{ \frac{-160}{819} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{10})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{21}{10}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x- \frac{63}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{-63} & = & \color{red}{270x} +80 \\\Leftrightarrow & -1050x \color{red}{-63} \color{blue}{+63} \color{blue}{-270x} & = & \color{red}{270x} +80 \color{blue}{-270x} \color{blue}{+63} \\\Leftrightarrow & -1050x-270x& = & 80+63 \\\Leftrightarrow & \color{red}{-1320} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1320} & & \\\Leftrightarrow & x = \frac{-13}{120} & & \\ & V = \left\{ \frac{-13}{120} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{+45} & = & \color{red}{-84x} +10 \\\Leftrightarrow & -72x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +10 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & -72x+84x& = & 10-45 \\\Leftrightarrow & \color{red}{12} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{12} & & \\ & V = \left\{ \frac{-35}{12} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{15}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+45} & = & \color{red}{231x} +88 \\\Leftrightarrow & 495x \color{red}{+45} \color{blue}{-45} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-45} \\\Leftrightarrow & 495x-231x& = & 88-45 \\\Leftrightarrow & \color{red}{264} x& = & 43 \\\Leftrightarrow & x = \frac{43}{264} & & \\ & V = \left\{ \frac{43}{264} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{11})& = & 6x+\frac{5}{11} \\\Leftrightarrow & -25x+\frac{10}{11}& = & 6x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{+10} & = & \color{red}{66x} +5 \\\Leftrightarrow & -275x \color{red}{+10} \color{blue}{-10} \color{blue}{-66x} & = & \color{red}{66x} +5 \color{blue}{-66x} \color{blue}{-10} \\\Leftrightarrow & -275x-66x& = & 5-10 \\\Leftrightarrow & \color{red}{-341} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-341} & & \\\Leftrightarrow & x = \frac{5}{341} & & \\ & V = \left\{ \frac{5}{341} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & 9x+\frac{7}{6} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+16} & = & \color{red}{54x} +7 \\\Leftrightarrow & 48x \color{red}{+16} \color{blue}{-16} \color{blue}{-54x} & = & \color{red}{54x} +7 \color{blue}{-54x} \color{blue}{-16} \\\Leftrightarrow & 48x-54x& = & 7-16 \\\Leftrightarrow & \color{red}{-6} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-6} & & \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+42} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -420x \color{red}{+42} \color{blue}{-42} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-42} \\\Leftrightarrow & -420x+175x& = & 15-42 \\\Leftrightarrow & \color{red}{-245} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-245} & & \\\Leftrightarrow & x = \frac{27}{245} & & \\ & V = \left\{ \frac{27}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +20 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 20-132 \\\Leftrightarrow & \color{red}{-935} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{-935} & & \\\Leftrightarrow & x = \frac{112}{935} & & \\ & V = \left\{ \frac{112}{935} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -9x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+28} & = & \color{red}{-108x} +9 \\\Leftrightarrow & 420x \color{red}{+28} \color{blue}{-28} \color{blue}{+108x} & = & \color{red}{-108x} +9 \color{blue}{+108x} \color{blue}{-28} \\\Leftrightarrow & 420x+108x& = & 9-28 \\\Leftrightarrow & \color{red}{528} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{528} & & \\ & V = \left\{ \frac{-19}{528} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+32} & = & \color{red}{252x} +21 \\\Leftrightarrow & -216x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -216x-252x& = & 21-32 \\\Leftrightarrow & \color{red}{-468} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-468} & & \\\Leftrightarrow & x = \frac{11}{468} & & \\ & V = \left\{ \frac{11}{468} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{9})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-8} & = & \color{red}{81x} +2 \\\Leftrightarrow & 180x \color{red}{-8} \color{blue}{+8} \color{blue}{-81x} & = & \color{red}{81x} +2 \color{blue}{-81x} \color{blue}{+8} \\\Leftrightarrow & 180x-81x& = & 2+8 \\\Leftrightarrow & \color{red}{99} x& = & 10 \\\Leftrightarrow & x = \frac{10}{99} & & \\ & V = \left\{ \frac{10}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{15}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-45} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -210x \color{red}{-45} \color{blue}{+45} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+45} \\\Leftrightarrow & -210x+147x& = & 70+45 \\\Leftrightarrow & \color{red}{-63} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-63} & & \\\Leftrightarrow & x = \frac{-115}{63} & & \\ & V = \left\{ \frac{-115}{63} \right\} & \\\end{align}\)