Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-10} & = & \color{red}{99x} +4 \\\Leftrightarrow & 110x \color{red}{-10} \color{blue}{+10} \color{blue}{-99x} & = & \color{red}{99x} +4 \color{blue}{-99x} \color{blue}{+10} \\\Leftrightarrow & 110x-99x& = & 4+10 \\\Leftrightarrow & \color{red}{11} x& = & 14 \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+100} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -875x \color{red}{+100} \color{blue}{-100} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-100} \\\Leftrightarrow & -875x+315x& = & 14-100 \\\Leftrightarrow & \color{red}{-560} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-560} & & \\\Leftrightarrow & x = \frac{43}{280} & & \\ & V = \left\{ \frac{43}{280} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{-255} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-255} & & \\\Leftrightarrow & x = \frac{-46}{255} & & \\ & V = \left\{ \frac{-46}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-56} & = & \color{red}{162x} +27 \\\Leftrightarrow & 252x \color{red}{-56} \color{blue}{+56} \color{blue}{-162x} & = & \color{red}{162x} +27 \color{blue}{-162x} \color{blue}{+56} \\\Leftrightarrow & 252x-162x& = & 27+56 \\\Leftrightarrow & \color{red}{90} x& = & 83 \\\Leftrightarrow & x = \frac{83}{90} & & \\ & V = \left\{ \frac{83}{90} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -28x+\frac{14}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{+14} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -140x \color{red}{+14} \color{blue}{-14} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-14} \\\Leftrightarrow & -140x+35x& = & 4-14 \\\Leftrightarrow & \color{red}{-105} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-105} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-40} & = & \color{red}{315x} +36 \\\Leftrightarrow & -450x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +36 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -450x-315x& = & 36+40 \\\Leftrightarrow & \color{red}{-765} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-765} & & \\\Leftrightarrow & x = \frac{-76}{765} & & \\ & V = \left\{ \frac{-76}{765} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{9})& = & 6x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{28}{9}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-308} & = & \color{red}{594x} +54 \\\Leftrightarrow & 3465x \color{red}{-308} \color{blue}{+308} \color{blue}{-594x} & = & \color{red}{594x} +54 \color{blue}{-594x} \color{blue}{+308} \\\Leftrightarrow & 3465x-594x& = & 54+308 \\\Leftrightarrow & \color{red}{2871} x& = & 362 \\\Leftrightarrow & x = \frac{362}{2871} & & \\ & V = \left\{ \frac{362}{2871} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{5})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{-12} & = & \color{red}{10x} +6 \\\Leftrightarrow & 75x \color{red}{-12} \color{blue}{+12} \color{blue}{-10x} & = & \color{red}{10x} +6 \color{blue}{-10x} \color{blue}{+12} \\\Leftrightarrow & 75x-10x& = & 6+12 \\\Leftrightarrow & \color{red}{65} x& = & 18 \\\Leftrightarrow & x = \frac{18}{65} & & \\ & V = \left\{ \frac{18}{65} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{4}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-4} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -40x \color{red}{-4} \color{blue}{+4} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+4} \\\Leftrightarrow & -40x+45x& = & 6+4 \\\Leftrightarrow & \color{red}{5} x& = & 10 \\\Leftrightarrow & x = \frac{10}{5} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{11})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{25}{11}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{50}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+50} & = & \color{red}{-44x} +33 \\\Leftrightarrow & 550x \color{red}{+50} \color{blue}{-50} \color{blue}{+44x} & = & \color{red}{-44x} +33 \color{blue}{+44x} \color{blue}{-50} \\\Leftrightarrow & 550x+44x& = & 33-50 \\\Leftrightarrow & \color{red}{594} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{594} & & \\ & V = \left\{ \frac{-17}{594} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{3})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 8x-\frac{16}{3}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-16} & = & \color{red}{-21x} +7 \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+21x} & = & \color{red}{-21x} +7 \color{blue}{+21x} \color{blue}{+16} \\\Leftrightarrow & 24x+21x& = & 7+16 \\\Leftrightarrow & \color{red}{45} x& = & 23 \\\Leftrightarrow & x = \frac{23}{45} & & \\ & V = \left\{ \frac{23}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{2})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 6x+\frac{15}{2}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{+165} & = & \color{red}{110x} +20 \\\Leftrightarrow & 132x \color{red}{+165} \color{blue}{-165} \color{blue}{-110x} & = & \color{red}{110x} +20 \color{blue}{-110x} \color{blue}{-165} \\\Leftrightarrow & 132x-110x& = & 20-165 \\\Leftrightarrow & \color{red}{22} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{22} & & \\ & V = \left\{ \frac{-145}{22} \right\} & \\\end{align}\)