Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{11})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{35}{11}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+105} & = & \color{red}{264x} +22 \\\Leftrightarrow & -693x \color{red}{+105} \color{blue}{-105} \color{blue}{-264x} & = & \color{red}{264x} +22 \color{blue}{-264x} \color{blue}{-105} \\\Leftrightarrow & -693x-264x& = & 22-105 \\\Leftrightarrow & \color{red}{-957} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-957} & & \\\Leftrightarrow & x = \frac{83}{957} & & \\ & V = \left\{ \frac{83}{957} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -14x+\frac{28}{9}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{-54x} +45 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{+54x} & = & \color{red}{-54x} +45 \color{blue}{+54x} \color{blue}{-56} \\\Leftrightarrow & -252x+54x& = & 45-56 \\\Leftrightarrow & \color{red}{-198} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-198} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{154x} +77 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{+60} \\\Leftrightarrow & -660x-154x& = & 77+60 \\\Leftrightarrow & \color{red}{-814} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-814} & & \\\Leftrightarrow & x = \frac{-137}{814} & & \\ & V = \left\{ \frac{-137}{814} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{16}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-32} & = & \color{red}{54x} +9 \\\Leftrightarrow & -48x \color{red}{-32} \color{blue}{+32} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{+32} \\\Leftrightarrow & -48x-54x& = & 9+32 \\\Leftrightarrow & \color{red}{-102} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-102} & & \\\Leftrightarrow & x = \frac{-41}{102} & & \\ & V = \left\{ \frac{-41}{102} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -135x-75x& = & 50-36 \\\Leftrightarrow & \color{red}{-210} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-210} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{4})& = & -4x+\frac{5}{3} \\\Leftrightarrow & 21x+\frac{21}{4}& = & -4x+\frac{5}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x+ \frac{63}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{20}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{+63} & = & \color{red}{-48x} +20 \\\Leftrightarrow & 252x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +20 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 252x+48x& = & 20-63 \\\Leftrightarrow & \color{red}{300} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{300} & & \\ & V = \left\{ \frac{-43}{300} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{5})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-28} & = & \color{red}{315x} +50 \\\Leftrightarrow & 280x \color{red}{-28} \color{blue}{+28} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+28} \\\Leftrightarrow & 280x-315x& = & 50+28 \\\Leftrightarrow & \color{red}{-35} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-35} & & \\\Leftrightarrow & x = \frac{-78}{35} & & \\ & V = \left\{ \frac{-78}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & 3x+\frac{7}{5} \\\Leftrightarrow & 10x+\frac{15}{8}& = & 3x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{400}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{120x} +56 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{-120x} & = & \color{red}{120x} +56 \color{blue}{-120x} \color{blue}{-75} \\\Leftrightarrow & 400x-120x& = & 56-75 \\\Leftrightarrow & \color{red}{280} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{280} & & \\ & V = \left\{ \frac{-19}{280} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+6} & = & \color{red}{55x} +6 \\\Leftrightarrow & -99x \color{red}{+6} \color{blue}{-6} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-6} \\\Leftrightarrow & -99x-55x& = & 6-6 \\\Leftrightarrow & \color{red}{-154} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-154} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+200} & = & \color{red}{90x} +27 \\\Leftrightarrow & -600x \color{red}{+200} \color{blue}{-200} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-200} \\\Leftrightarrow & -600x-90x& = & 27-200 \\\Leftrightarrow & \color{red}{-690} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-690} & & \\\Leftrightarrow & x = \frac{173}{690} & & \\ & V = \left\{ \frac{173}{690} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-110x} +77 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & -264x+110x& = & 77+24 \\\Leftrightarrow & \color{red}{-154} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-154} & & \\\Leftrightarrow & x = \frac{-101}{154} & & \\ & V = \left\{ \frac{-101}{154} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -270x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{45} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{45} & & \\ & V = \left\{ \frac{-58}{45} \right\} & \\\end{align}\)