Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 25-132 \\\Leftrightarrow & \color{red}{-385} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-385} & & \\\Leftrightarrow & x = \frac{107}{385} & & \\ & V = \left\{ \frac{107}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{18}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+54} & = & \color{red}{105x} +14 \\\Leftrightarrow & -252x \color{red}{+54} \color{blue}{-54} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-54} \\\Leftrightarrow & -252x-105x& = & 14-54 \\\Leftrightarrow & \color{red}{-357} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-357} & & \\\Leftrightarrow & x = \frac{40}{357} & & \\ & V = \left\{ \frac{40}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -14x+\frac{14}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{+98} & = & \color{red}{105x} +20 \\\Leftrightarrow & -490x \color{red}{+98} \color{blue}{-98} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-98} \\\Leftrightarrow & -490x-105x& = & 20-98 \\\Leftrightarrow & \color{red}{-595} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-595} & & \\\Leftrightarrow & x = \frac{78}{595} & & \\ & V = \left\{ \frac{78}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 6x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{198x} +18 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-198x} & = & \color{red}{198x} +18 \color{blue}{-198x} \color{blue}{+154} \\\Leftrightarrow & -1155x-198x& = & 18+154 \\\Leftrightarrow & \color{red}{-1353} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1353} & & \\\Leftrightarrow & x = \frac{-172}{1353} & & \\ & V = \left\{ \frac{-172}{1353} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{+45} & = & \color{red}{60x} +40 \\\Leftrightarrow & -144x \color{red}{+45} \color{blue}{-45} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{-45} \\\Leftrightarrow & -144x-60x& = & 40-45 \\\Leftrightarrow & \color{red}{-204} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-204} & & \\\Leftrightarrow & x = \frac{5}{204} & & \\ & V = \left\{ \frac{5}{204} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{6})& = & -3x+\frac{2}{7} \\\Leftrightarrow & -20x-\frac{25}{6}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{-126}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{-126x} +12 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{+126x} & = & \color{red}{-126x} +12 \color{blue}{+126x} \color{blue}{+175} \\\Leftrightarrow & -840x+126x& = & 12+175 \\\Leftrightarrow & \color{red}{-714} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-714} & & \\\Leftrightarrow & x = \frac{-11}{42} & & \\ & V = \left\{ \frac{-11}{42} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{7})& = & -9x+\frac{2}{5} \\\Leftrightarrow & 8x+\frac{12}{7}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+60} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 280x \color{red}{+60} \color{blue}{-60} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-60} \\\Leftrightarrow & 280x+315x& = & 14-60 \\\Leftrightarrow & \color{red}{595} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{595} & & \\ & V = \left\{ \frac{-46}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -20x-\frac{8}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{135x} +6 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -300x-135x& = & 6+40 \\\Leftrightarrow & \color{red}{-435} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-435} & & \\\Leftrightarrow & x = \frac{-46}{435} & & \\ & V = \left\{ \frac{-46}{435} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+80} & = & \color{red}{275x} +44 \\\Leftrightarrow & 440x \color{red}{+80} \color{blue}{-80} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{-80} \\\Leftrightarrow & 440x-275x& = & 44-80 \\\Leftrightarrow & \color{red}{165} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{165} & & \\\Leftrightarrow & x = \frac{-12}{55} & & \\ & V = \left\{ \frac{-12}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 4x-\frac{6}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-42} & = & \color{red}{-175x} +45 \\\Leftrightarrow & 140x \color{red}{-42} \color{blue}{+42} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{+42} \\\Leftrightarrow & 140x+175x& = & 45+42 \\\Leftrightarrow & \color{red}{315} x& = & 87 \\\Leftrightarrow & x = \frac{87}{315} & & \\\Leftrightarrow & x = \frac{29}{105} & & \\ & V = \left\{ \frac{29}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-280}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{-60} & = & \color{red}{-350x} +21 \\\Leftrightarrow & -280x \color{red}{-60} \color{blue}{+60} \color{blue}{+350x} & = & \color{red}{-350x} +21 \color{blue}{+350x} \color{blue}{+60} \\\Leftrightarrow & -280x+350x& = & 21+60 \\\Leftrightarrow & \color{red}{70} x& = & 81 \\\Leftrightarrow & x = \frac{81}{70} & & \\ & V = \left\{ \frac{81}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+42} & = & \color{red}{-81x} +2 \\\Leftrightarrow & 126x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +2 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & 126x+81x& = & 2-42 \\\Leftrightarrow & \color{red}{207} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{207} & & \\ & V = \left\{ \frac{-40}{207} \right\} & \\\end{align}\)