Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & -35x-\frac{14}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1540}{ \color{blue}{44} }x- \frac{56}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1540x \color{red}{-56} & = & \color{red}{132x} +33 \\\Leftrightarrow & -1540x \color{red}{-56} \color{blue}{+56} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{+56} \\\Leftrightarrow & -1540x-132x& = & 33+56 \\\Leftrightarrow & \color{red}{-1672} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-1672} & & \\\Leftrightarrow & x = \frac{-89}{1672} & & \\ & V = \left\{ \frac{-89}{1672} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{10})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{9}{10}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-9} & = & \color{red}{50x} +3 \\\Leftrightarrow & 60x \color{red}{-9} \color{blue}{+9} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{+9} \\\Leftrightarrow & 60x-50x& = & 3+9 \\\Leftrightarrow & \color{red}{10} x& = & 12 \\\Leftrightarrow & x = \frac{12}{10} & & \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 8x+\frac{3}{11} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 8x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-154} & = & \color{red}{264x} +9 \\\Leftrightarrow & -924x \color{red}{-154} \color{blue}{+154} \color{blue}{-264x} & = & \color{red}{264x} +9 \color{blue}{-264x} \color{blue}{+154} \\\Leftrightarrow & -924x-264x& = & 9+154 \\\Leftrightarrow & \color{red}{-1188} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-1188} & & \\\Leftrightarrow & x = \frac{-163}{1188} & & \\ & V = \left\{ \frac{-163}{1188} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{18}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{90}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{245x} +14 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-90} \\\Leftrightarrow & -630x-245x& = & 14-90 \\\Leftrightarrow & \color{red}{-875} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-875} & & \\\Leftrightarrow & x = \frac{76}{875} & & \\ & V = \left\{ \frac{76}{875} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{15}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-45} & = & \color{red}{-105x} +35 \\\Leftrightarrow & -252x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & -252x+105x& = & 35+45 \\\Leftrightarrow & \color{red}{-147} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-147} & & \\\Leftrightarrow & x = \frac{-80}{147} & & \\ & V = \left\{ \frac{-80}{147} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x- \frac{108}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{-108} & = & \color{red}{300x} +35 \\\Leftrightarrow & 720x \color{red}{-108} \color{blue}{+108} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{+108} \\\Leftrightarrow & 720x-300x& = & 35+108 \\\Leftrightarrow & \color{red}{420} x& = & 143 \\\Leftrightarrow & x = \frac{143}{420} & & \\ & V = \left\{ \frac{143}{420} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{-80} & = & \color{red}{-392x} +49 \\\Leftrightarrow & -560x \color{red}{-80} \color{blue}{+80} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{+80} \\\Leftrightarrow & -560x+392x& = & 49+80 \\\Leftrightarrow & \color{red}{-168} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-168} & & \\\Leftrightarrow & x = \frac{-43}{56} & & \\ & V = \left\{ \frac{-43}{56} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{5})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{-28} & = & \color{red}{20x} +15 \\\Leftrightarrow & 350x \color{red}{-28} \color{blue}{+28} \color{blue}{-20x} & = & \color{red}{20x} +15 \color{blue}{-20x} \color{blue}{+28} \\\Leftrightarrow & 350x-20x& = & 15+28 \\\Leftrightarrow & \color{red}{330} x& = & 43 \\\Leftrightarrow & x = \frac{43}{330} & & \\ & V = \left\{ \frac{43}{330} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-960}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -960x \color{red}{+144} & = & \color{red}{-420x} +35 \\\Leftrightarrow & -960x \color{red}{+144} \color{blue}{-144} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{-144} \\\Leftrightarrow & -960x+420x& = & 35-144 \\\Leftrightarrow & \color{red}{-540} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-540} & & \\\Leftrightarrow & x = \frac{109}{540} & & \\ & V = \left\{ \frac{109}{540} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & 396x+165x& = & 88-54 \\\Leftrightarrow & \color{red}{561} x& = & 34 \\\Leftrightarrow & x = \frac{34}{561} & & \\\Leftrightarrow & x = \frac{2}{33} & & \\ & V = \left\{ \frac{2}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{25x} +4 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 90x-25x& = & 4+24 \\\Leftrightarrow & \color{red}{65} x& = & 28 \\\Leftrightarrow & x = \frac{28}{65} & & \\ & V = \left\{ \frac{28}{65} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-60} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 180x \color{red}{-60} \color{blue}{+60} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{+60} \\\Leftrightarrow & 180x+81x& = & 10+60 \\\Leftrightarrow & \color{red}{261} x& = & 70 \\\Leftrightarrow & x = \frac{70}{261} & & \\ & V = \left\{ \frac{70}{261} \right\} & \\\end{align}\)