Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-12} & = & \color{red}{-40x} +6 \\\Leftrightarrow & -75x \color{red}{-12} \color{blue}{+12} \color{blue}{+40x} & = & \color{red}{-40x} +6 \color{blue}{+40x} \color{blue}{+12} \\\Leftrightarrow & -75x+40x& = & 6+12 \\\Leftrightarrow & \color{red}{-35} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-35} & & \\\Leftrightarrow & x = \frac{-18}{35} & & \\ & V = \left\{ \frac{-18}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-8} & = & \color{red}{21x} +8 \\\Leftrightarrow & -30x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & -30x-21x& = & 8+8 \\\Leftrightarrow & \color{red}{-51} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-51} & & \\\Leftrightarrow & x = \frac{-16}{51} & & \\ & V = \left\{ \frac{-16}{51} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1080}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1080x \color{red}{-216} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 1080x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 1080x+225x& = & 40+216 \\\Leftrightarrow & \color{red}{1305} x& = & 256 \\\Leftrightarrow & x = \frac{256}{1305} & & \\ & V = \left\{ \frac{256}{1305} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{9})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{275}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+275} & = & \color{red}{-297x} +81 \\\Leftrightarrow & -1980x \color{red}{+275} \color{blue}{-275} \color{blue}{+297x} & = & \color{red}{-297x} +81 \color{blue}{+297x} \color{blue}{-275} \\\Leftrightarrow & -1980x+297x& = & 81-275 \\\Leftrightarrow & \color{red}{-1683} x& = & -194 \\\Leftrightarrow & x = \frac{-194}{-1683} & & \\\Leftrightarrow & x = \frac{194}{1683} & & \\ & V = \left\{ \frac{194}{1683} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+18} & = & \color{red}{231x} +88 \\\Leftrightarrow & -198x \color{red}{+18} \color{blue}{-18} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-18} \\\Leftrightarrow & -198x-231x& = & 88-18 \\\Leftrightarrow & \color{red}{-429} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-429} & & \\\Leftrightarrow & x = \frac{-70}{429} & & \\ & V = \left\{ \frac{-70}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x+\frac{6}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+6} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -44x \color{red}{+6} \color{blue}{-6} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-6} \\\Leftrightarrow & -44x+99x& = & 6-6 \\\Leftrightarrow & \color{red}{55} x& = & 0 \\\Leftrightarrow & x = \frac{0}{55} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-198} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 660x \color{red}{-198} \color{blue}{+198} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+198} \\\Leftrightarrow & 660x+275x& = & 50+198 \\\Leftrightarrow & \color{red}{935} x& = & 248 \\\Leftrightarrow & x = \frac{248}{935} & & \\ & V = \left\{ \frac{248}{935} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & 4x+\frac{4}{9} \\\Leftrightarrow & 9x-\frac{15}{11}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{891}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 891x \color{red}{-135} & = & \color{red}{396x} +44 \\\Leftrightarrow & 891x \color{red}{-135} \color{blue}{+135} \color{blue}{-396x} & = & \color{red}{396x} +44 \color{blue}{-396x} \color{blue}{+135} \\\Leftrightarrow & 891x-396x& = & 44+135 \\\Leftrightarrow & \color{red}{495} x& = & 179 \\\Leftrightarrow & x = \frac{179}{495} & & \\ & V = \left\{ \frac{179}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{-280x} +49 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{-48} \\\Leftrightarrow & 336x+280x& = & 49-48 \\\Leftrightarrow & \color{red}{616} x& = & 1 \\\Leftrightarrow & x = \frac{1}{616} & & \\ & V = \left\{ \frac{1}{616} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+60} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -525x \color{red}{+60} \color{blue}{-60} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{-60} \\\Leftrightarrow & -525x+189x& = & 56-60 \\\Leftrightarrow & \color{red}{-336} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-336} & & \\\Leftrightarrow & x = \frac{1}{84} & & \\ & V = \left\{ \frac{1}{84} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{6})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -14x+\frac{35}{6}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{-90x} +9 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{+90x} & = & \color{red}{-90x} +9 \color{blue}{+90x} \color{blue}{-175} \\\Leftrightarrow & -420x+90x& = & 9-175 \\\Leftrightarrow & \color{red}{-330} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-330} & & \\\Leftrightarrow & x = \frac{83}{165} & & \\ & V = \left\{ \frac{83}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{50x} +15 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+36} \\\Leftrightarrow & 120x-50x& = & 15+36 \\\Leftrightarrow & \color{red}{70} x& = & 51 \\\Leftrightarrow & x = \frac{51}{70} & & \\ & V = \left\{ \frac{51}{70} \right\} & \\\end{align}\)