Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 90x+63x& = & 6+8 \\\Leftrightarrow & \color{red}{153} x& = & 14 \\\Leftrightarrow & x = \frac{14}{153} & & \\ & V = \left\{ \frac{14}{153} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -4x+\frac{2}{11} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+66} & = & \color{red}{-308x} +14 \\\Leftrightarrow & 693x \color{red}{+66} \color{blue}{-66} \color{blue}{+308x} & = & \color{red}{-308x} +14 \color{blue}{+308x} \color{blue}{-66} \\\Leftrightarrow & 693x+308x& = & 14-66 \\\Leftrightarrow & \color{red}{1001} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{1001} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{10}{3}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-110} & = & \color{red}{-165x} +15 \\\Leftrightarrow & 198x \color{red}{-110} \color{blue}{+110} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{+110} \\\Leftrightarrow & 198x+165x& = & 15+110 \\\Leftrightarrow & \color{red}{363} x& = & 125 \\\Leftrightarrow & x = \frac{125}{363} & & \\ & V = \left\{ \frac{125}{363} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{105x} +20 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-12} \\\Leftrightarrow & -150x-105x& = & 20-12 \\\Leftrightarrow & \color{red}{-255} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-255} & & \\\Leftrightarrow & x = \frac{-8}{255} & & \\ & V = \left\{ \frac{-8}{255} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{70x} +3 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 300x-70x& = & 3+24 \\\Leftrightarrow & \color{red}{230} x& = & 27 \\\Leftrightarrow & x = \frac{27}{230} & & \\ & V = \left\{ \frac{27}{230} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x+\frac{6}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+30} & = & \color{red}{275x} +22 \\\Leftrightarrow & 660x \color{red}{+30} \color{blue}{-30} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-30} \\\Leftrightarrow & 660x-275x& = & 22-30 \\\Leftrightarrow & \color{red}{385} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{385} & & \\ & V = \left\{ \frac{-8}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-60} & = & \color{red}{63x} +10 \\\Leftrightarrow & -180x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & -180x-63x& = & 10+60 \\\Leftrightarrow & \color{red}{-243} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-243} & & \\\Leftrightarrow & x = \frac{-70}{243} & & \\ & V = \left\{ \frac{-70}{243} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{20}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+100} & = & \color{red}{245x} +63 \\\Leftrightarrow & 525x \color{red}{+100} \color{blue}{-100} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-100} \\\Leftrightarrow & 525x-245x& = & 63-100 \\\Leftrightarrow & \color{red}{280} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{280} & & \\ & V = \left\{ \frac{-37}{280} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -324x \color{red}{+135} & = & \color{red}{-180x} +40 \\\Leftrightarrow & -324x \color{red}{+135} \color{blue}{-135} \color{blue}{+180x} & = & \color{red}{-180x} +40 \color{blue}{+180x} \color{blue}{-135} \\\Leftrightarrow & -324x+180x& = & 40-135 \\\Leftrightarrow & \color{red}{-144} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-144} & & \\\Leftrightarrow & x = \frac{95}{144} & & \\ & V = \left\{ \frac{95}{144} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{6})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{35}{6}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+35} & = & \color{red}{18x} +16 \\\Leftrightarrow & -84x \color{red}{+35} \color{blue}{-35} \color{blue}{-18x} & = & \color{red}{18x} +16 \color{blue}{-18x} \color{blue}{-35} \\\Leftrightarrow & -84x-18x& = & 16-35 \\\Leftrightarrow & \color{red}{-102} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-102} & & \\\Leftrightarrow & x = \frac{19}{102} & & \\ & V = \left\{ \frac{19}{102} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{7})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 18x-\frac{24}{7}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-72} & = & \color{red}{-147x} +49 \\\Leftrightarrow & 378x \color{red}{-72} \color{blue}{+72} \color{blue}{+147x} & = & \color{red}{-147x} +49 \color{blue}{+147x} \color{blue}{+72} \\\Leftrightarrow & 378x+147x& = & 49+72 \\\Leftrightarrow & \color{red}{525} x& = & 121 \\\Leftrightarrow & x = \frac{121}{525} & & \\ & V = \left\{ \frac{121}{525} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-1)& = & -9x+\frac{5}{6} \\\Leftrightarrow & -35x+7& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 1 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{42}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{-54x} +5 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-42} \\\Leftrightarrow & -210x+54x& = & 5-42 \\\Leftrightarrow & \color{red}{-156} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-156} & & \\\Leftrightarrow & x = \frac{37}{156} & & \\ & V = \left\{ \frac{37}{156} \right\} & \\\end{align}\)