Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{1}{2})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -28x+\frac{7}{2}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+63} & = & \color{red}{-144x} +8 \\\Leftrightarrow & -504x \color{red}{+63} \color{blue}{-63} \color{blue}{+144x} & = & \color{red}{-144x} +8 \color{blue}{+144x} \color{blue}{-63} \\\Leftrightarrow & -504x+144x& = & 8-63 \\\Leftrightarrow & \color{red}{-360} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-360} & & \\\Leftrightarrow & x = \frac{11}{72} & & \\ & V = \left\{ \frac{11}{72} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{9})& = & -8x+\frac{5}{6} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{-40} & = & \color{red}{-144x} +15 \\\Leftrightarrow & -270x \color{red}{-40} \color{blue}{+40} \color{blue}{+144x} & = & \color{red}{-144x} +15 \color{blue}{+144x} \color{blue}{+40} \\\Leftrightarrow & -270x+144x& = & 15+40 \\\Leftrightarrow & \color{red}{-126} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-126} & & \\\Leftrightarrow & x = \frac{-55}{126} & & \\ & V = \left\{ \frac{-55}{126} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -9x+\frac{9}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+63} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -315x \color{red}{+63} \color{blue}{-63} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-63} \\\Leftrightarrow & -315x+245x& = & 50-63 \\\Leftrightarrow & \color{red}{-70} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-70} & & \\\Leftrightarrow & x = \frac{13}{70} & & \\ & V = \left\{ \frac{13}{70} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{-24x} +40 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{+24x} & = & \color{red}{-24x} +40 \color{blue}{+24x} \color{blue}{+45} \\\Leftrightarrow & 180x+24x& = & 40+45 \\\Leftrightarrow & \color{red}{204} x& = & 85 \\\Leftrightarrow & x = \frac{85}{204} & & \\\Leftrightarrow & x = \frac{5}{12} & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-80} & = & \color{red}{-315x} +42 \\\Leftrightarrow & -280x \color{red}{-80} \color{blue}{+80} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{+80} \\\Leftrightarrow & -280x+315x& = & 42+80 \\\Leftrightarrow & \color{red}{35} x& = & 122 \\\Leftrightarrow & x = \frac{122}{35} & & \\ & V = \left\{ \frac{122}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{4})& = & -8x+\frac{8}{9} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-288}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{+135} & = & \color{red}{-288x} +32 \\\Leftrightarrow & 324x \color{red}{+135} \color{blue}{-135} \color{blue}{+288x} & = & \color{red}{-288x} +32 \color{blue}{+288x} \color{blue}{-135} \\\Leftrightarrow & 324x+288x& = & 32-135 \\\Leftrightarrow & \color{red}{612} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{612} & & \\ & V = \left\{ \frac{-103}{612} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{25}{6}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+125} & = & \color{red}{-210x} +48 \\\Leftrightarrow & 300x \color{red}{+125} \color{blue}{-125} \color{blue}{+210x} & = & \color{red}{-210x} +48 \color{blue}{+210x} \color{blue}{-125} \\\Leftrightarrow & 300x+210x& = & 48-125 \\\Leftrightarrow & \color{red}{510} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{510} & & \\ & V = \left\{ \frac{-77}{510} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{4})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-165} & = & \color{red}{-308x} +16 \\\Leftrightarrow & 1100x \color{red}{-165} \color{blue}{+165} \color{blue}{+308x} & = & \color{red}{-308x} +16 \color{blue}{+308x} \color{blue}{+165} \\\Leftrightarrow & 1100x+308x& = & 16+165 \\\Leftrightarrow & \color{red}{1408} x& = & 181 \\\Leftrightarrow & x = \frac{181}{1408} & & \\ & V = \left\{ \frac{181}{1408} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{9})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{-8} & = & \color{red}{90x} +27 \\\Leftrightarrow & 108x \color{red}{-8} \color{blue}{+8} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{+8} \\\Leftrightarrow & 108x-90x& = & 27+8 \\\Leftrightarrow & \color{red}{18} x& = & 35 \\\Leftrightarrow & x = \frac{35}{18} & & \\ & V = \left\{ \frac{35}{18} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 126x+147x& = & 14+18 \\\Leftrightarrow & \color{red}{273} x& = & 32 \\\Leftrightarrow & x = \frac{32}{273} & & \\ & V = \left\{ \frac{32}{273} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & 4x+\frac{5}{4} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 4x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-40} & = & \color{red}{176x} +55 \\\Leftrightarrow & 1100x \color{red}{-40} \color{blue}{+40} \color{blue}{-176x} & = & \color{red}{176x} +55 \color{blue}{-176x} \color{blue}{+40} \\\Leftrightarrow & 1100x-176x& = & 55+40 \\\Leftrightarrow & \color{red}{924} x& = & 95 \\\Leftrightarrow & x = \frac{95}{924} & & \\ & V = \left\{ \frac{95}{924} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{10})& = & 4x+\frac{7}{5} \\\Leftrightarrow & 21x-\frac{21}{10}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{21}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-21} & = & \color{red}{40x} +14 \\\Leftrightarrow & 210x \color{red}{-21} \color{blue}{+21} \color{blue}{-40x} & = & \color{red}{40x} +14 \color{blue}{-40x} \color{blue}{+21} \\\Leftrightarrow & 210x-40x& = & 14+21 \\\Leftrightarrow & \color{red}{170} x& = & 35 \\\Leftrightarrow & x = \frac{35}{170} & & \\\Leftrightarrow & x = \frac{7}{34} & & \\ & V = \left\{ \frac{7}{34} \right\} & \\\end{align}\)