Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{11})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 20x+\frac{15}{11}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+75} & = & \color{red}{165x} +22 \\\Leftrightarrow & 1100x \color{red}{+75} \color{blue}{-75} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{-75} \\\Leftrightarrow & 1100x-165x& = & 22-75 \\\Leftrightarrow & \color{red}{935} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{935} & & \\ & V = \left\{ \frac{-53}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & -9x+\frac{9}{5} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+40} & = & \color{red}{-135x} +27 \\\Leftrightarrow & -300x \color{red}{+40} \color{blue}{-40} \color{blue}{+135x} & = & \color{red}{-135x} +27 \color{blue}{+135x} \color{blue}{-40} \\\Leftrightarrow & -300x+135x& = & 27-40 \\\Leftrightarrow & \color{red}{-165} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-165} & & \\\Leftrightarrow & x = \frac{13}{165} & & \\ & V = \left\{ \frac{13}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -14x+\frac{28}{9}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+308} & = & \color{red}{495x} +18 \\\Leftrightarrow & -1386x \color{red}{+308} \color{blue}{-308} \color{blue}{-495x} & = & \color{red}{495x} +18 \color{blue}{-495x} \color{blue}{-308} \\\Leftrightarrow & -1386x-495x& = & 18-308 \\\Leftrightarrow & \color{red}{-1881} x& = & -290 \\\Leftrightarrow & x = \frac{-290}{-1881} & & \\\Leftrightarrow & x = \frac{290}{1881} & & \\ & V = \left\{ \frac{290}{1881} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{-196} & = & \color{red}{-315x} +27 \\\Leftrightarrow & 1764x \color{red}{-196} \color{blue}{+196} \color{blue}{+315x} & = & \color{red}{-315x} +27 \color{blue}{+315x} \color{blue}{+196} \\\Leftrightarrow & 1764x+315x& = & 27+196 \\\Leftrightarrow & \color{red}{2079} x& = & 223 \\\Leftrightarrow & x = \frac{223}{2079} & & \\ & V = \left\{ \frac{223}{2079} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{9})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{4}{9}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+40} & = & \color{red}{-270x} +27 \\\Leftrightarrow & -720x \color{red}{+40} \color{blue}{-40} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{-40} \\\Leftrightarrow & -720x+270x& = & 27-40 \\\Leftrightarrow & \color{red}{-450} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-450} & & \\\Leftrightarrow & x = \frac{13}{450} & & \\ & V = \left\{ \frac{13}{450} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{5})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{16}{5}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{48}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+48} & = & \color{red}{-45x} +40 \\\Leftrightarrow & 300x \color{red}{+48} \color{blue}{-48} \color{blue}{+45x} & = & \color{red}{-45x} +40 \color{blue}{+45x} \color{blue}{-48} \\\Leftrightarrow & 300x+45x& = & 40-48 \\\Leftrightarrow & \color{red}{345} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{345} & & \\ & V = \left\{ \frac{-8}{345} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x-\frac{15}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-45} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 252x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & 252x+105x& = & 35+45 \\\Leftrightarrow & \color{red}{357} x& = & 80 \\\Leftrightarrow & x = \frac{80}{357} & & \\ & V = \left\{ \frac{80}{357} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-126} & = & \color{red}{693x} +33 \\\Leftrightarrow & -1386x \color{red}{-126} \color{blue}{+126} \color{blue}{-693x} & = & \color{red}{693x} +33 \color{blue}{-693x} \color{blue}{+126} \\\Leftrightarrow & -1386x-693x& = & 33+126 \\\Leftrightarrow & \color{red}{-2079} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-2079} & & \\\Leftrightarrow & x = \frac{-53}{693} & & \\ & V = \left\{ \frac{-53}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{5}{7} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+84} & = & \color{red}{140x} +25 \\\Leftrightarrow & -525x \color{red}{+84} \color{blue}{-84} \color{blue}{-140x} & = & \color{red}{140x} +25 \color{blue}{-140x} \color{blue}{-84} \\\Leftrightarrow & -525x-140x& = & 25-84 \\\Leftrightarrow & \color{red}{-665} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-665} & & \\\Leftrightarrow & x = \frac{59}{665} & & \\ & V = \left\{ \frac{59}{665} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -6x+\frac{3}{10} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -6x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{280}{ \color{blue}{30} })& = & (\frac{-180}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-280} & = & \color{red}{-180x} +9 \\\Leftrightarrow & 1050x \color{red}{-280} \color{blue}{+280} \color{blue}{+180x} & = & \color{red}{-180x} +9 \color{blue}{+180x} \color{blue}{+280} \\\Leftrightarrow & 1050x+180x& = & 9+280 \\\Leftrightarrow & \color{red}{1230} x& = & 289 \\\Leftrightarrow & x = \frac{289}{1230} & & \\ & V = \left\{ \frac{289}{1230} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -9x+\frac{9}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+81} & = & \color{red}{225x} +20 \\\Leftrightarrow & -405x \color{red}{+81} \color{blue}{-81} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-81} \\\Leftrightarrow & -405x-225x& = & 20-81 \\\Leftrightarrow & \color{red}{-630} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-630} & & \\\Leftrightarrow & x = \frac{61}{630} & & \\ & V = \left\{ \frac{61}{630} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{-300x} +25 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{-144} \\\Leftrightarrow & 720x+300x& = & 25-144 \\\Leftrightarrow & \color{red}{1020} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{1020} & & \\\Leftrightarrow & x = \frac{-7}{60} & & \\ & V = \left\{ \frac{-7}{60} \right\} & \\\end{align}\)