Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-99} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 660x \color{red}{-99} \color{blue}{+99} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+99} \\\Leftrightarrow & 660x+385x& = & 30+99 \\\Leftrightarrow & \color{red}{1045} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1045} & & \\ & V = \left\{ \frac{129}{1045} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 6x-\frac{9}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-81} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 270x \color{red}{-81} \color{blue}{+81} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+81} \\\Leftrightarrow & 270x+225x& = & 50+81 \\\Leftrightarrow & \color{red}{495} x& = & 131 \\\Leftrightarrow & x = \frac{131}{495} & & \\ & V = \left\{ \frac{131}{495} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-88} & = & \color{red}{-693x} +72 \\\Leftrightarrow & -594x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +72 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -594x+693x& = & 72+88 \\\Leftrightarrow & \color{red}{99} x& = & 160 \\\Leftrightarrow & x = \frac{160}{99} & & \\ & V = \left\{ \frac{160}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{11})& = & -9x+\frac{7}{11} \\\Leftrightarrow & 8x-\frac{6}{11}& = & -9x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-6} & = & \color{red}{-99x} +7 \\\Leftrightarrow & 88x \color{red}{-6} \color{blue}{+6} \color{blue}{+99x} & = & \color{red}{-99x} +7 \color{blue}{+99x} \color{blue}{+6} \\\Leftrightarrow & 88x+99x& = & 7+6 \\\Leftrightarrow & \color{red}{187} x& = & 13 \\\Leftrightarrow & x = \frac{13}{187} & & \\ & V = \left\{ \frac{13}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+10} & = & \color{red}{49x} +8 \\\Leftrightarrow & -140x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & -140x-49x& = & 8-10 \\\Leftrightarrow & \color{red}{-189} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-189} & & \\\Leftrightarrow & x = \frac{2}{189} & & \\ & V = \left\{ \frac{2}{189} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 14x-\frac{21}{2}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x- \frac{21}{ \color{blue}{2} })& = & (\frac{10}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{-21} & = & \color{red}{10x} +3 \\\Leftrightarrow & 28x \color{red}{-21} \color{blue}{+21} \color{blue}{-10x} & = & \color{red}{10x} +3 \color{blue}{-10x} \color{blue}{+21} \\\Leftrightarrow & 28x-10x& = & 3+21 \\\Leftrightarrow & \color{red}{18} x& = & 24 \\\Leftrightarrow & x = \frac{24}{18} & & \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{5}{8} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{+144} & = & \color{red}{-440x} +55 \\\Leftrightarrow & -1056x \color{red}{+144} \color{blue}{-144} \color{blue}{+440x} & = & \color{red}{-440x} +55 \color{blue}{+440x} \color{blue}{-144} \\\Leftrightarrow & -1056x+440x& = & 55-144 \\\Leftrightarrow & \color{red}{-616} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-616} & & \\\Leftrightarrow & x = \frac{89}{616} & & \\ & V = \left\{ \frac{89}{616} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{9})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{16}{9}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{64}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-64} & = & \color{red}{-252x} +27 \\\Leftrightarrow & -720x \color{red}{-64} \color{blue}{+64} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{+64} \\\Leftrightarrow & -720x+252x& = & 27+64 \\\Leftrightarrow & \color{red}{-468} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-468} & & \\\Leftrightarrow & x = \frac{-7}{36} & & \\ & V = \left\{ \frac{-7}{36} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{9})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{16}{9}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{32}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-32} & = & \color{red}{90x} +15 \\\Leftrightarrow & -216x \color{red}{-32} \color{blue}{+32} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+32} \\\Leftrightarrow & -216x-90x& = & 15+32 \\\Leftrightarrow & \color{red}{-306} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-306} & & \\\Leftrightarrow & x = \frac{-47}{306} & & \\ & V = \left\{ \frac{-47}{306} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{2}{7} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-84} & = & \color{red}{-280x} +10 \\\Leftrightarrow & -525x \color{red}{-84} \color{blue}{+84} \color{blue}{+280x} & = & \color{red}{-280x} +10 \color{blue}{+280x} \color{blue}{+84} \\\Leftrightarrow & -525x+280x& = & 10+84 \\\Leftrightarrow & \color{red}{-245} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-245} & & \\\Leftrightarrow & x = \frac{-94}{245} & & \\ & V = \left\{ \frac{-94}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{5})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 14x+\frac{28}{5}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{840}{ \color{blue}{60} }x+ \frac{336}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 840x \color{red}{+336} & = & \color{red}{180x} +35 \\\Leftrightarrow & 840x \color{red}{+336} \color{blue}{-336} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{-336} \\\Leftrightarrow & 840x-180x& = & 35-336 \\\Leftrightarrow & \color{red}{660} x& = & -301 \\\Leftrightarrow & x = \frac{-301}{660} & & \\ & V = \left\{ \frac{-301}{660} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 8x+\frac{16}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+48} & = & \color{red}{-63x} +7 \\\Leftrightarrow & 72x \color{red}{+48} \color{blue}{-48} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{-48} \\\Leftrightarrow & 72x+63x& = & 7-48 \\\Leftrightarrow & \color{red}{135} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{135} & & \\ & V = \left\{ \frac{-41}{135} \right\} & \\\end{align}\)