Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{11})& = & -3x+\frac{5}{6} \\\Leftrightarrow & 20x-\frac{25}{11}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1320}{ \color{blue}{66} }x- \frac{150}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1320x \color{red}{-150} & = & \color{red}{-198x} +55 \\\Leftrightarrow & 1320x \color{red}{-150} \color{blue}{+150} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{+150} \\\Leftrightarrow & 1320x+198x& = & 55+150 \\\Leftrightarrow & \color{red}{1518} x& = & 205 \\\Leftrightarrow & x = \frac{205}{1518} & & \\ & V = \left\{ \frac{205}{1518} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{8})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{15}{8}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+105} & = & \color{red}{-280x} +32 \\\Leftrightarrow & 336x \color{red}{+105} \color{blue}{-105} \color{blue}{+280x} & = & \color{red}{-280x} +32 \color{blue}{+280x} \color{blue}{-105} \\\Leftrightarrow & 336x+280x& = & 32-105 \\\Leftrightarrow & \color{red}{616} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{616} & & \\ & V = \left\{ \frac{-73}{616} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{-308x} +32 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +32 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -440x+308x& = & 32-165 \\\Leftrightarrow & \color{red}{-132} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-132} & & \\\Leftrightarrow & x = \frac{133}{132} & & \\ & V = \left\{ \frac{133}{132} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 28x-\frac{21}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x- \frac{210}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{-210} & = & \color{red}{-330x} +99 \\\Leftrightarrow & 3080x \color{red}{-210} \color{blue}{+210} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{+210} \\\Leftrightarrow & 3080x+330x& = & 99+210 \\\Leftrightarrow & \color{red}{3410} x& = & 309 \\\Leftrightarrow & x = \frac{309}{3410} & & \\ & V = \left\{ \frac{309}{3410} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{+270} & = & \color{red}{567x} +70 \\\Leftrightarrow & -1134x \color{red}{+270} \color{blue}{-270} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{-270} \\\Leftrightarrow & -1134x-567x& = & 70-270 \\\Leftrightarrow & \color{red}{-1701} x& = & -200 \\\Leftrightarrow & x = \frac{-200}{-1701} & & \\\Leftrightarrow & x = \frac{200}{1701} & & \\ & V = \left\{ \frac{200}{1701} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{12}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-12} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -220x \color{red}{-12} \color{blue}{+12} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+12} \\\Leftrightarrow & -220x+77x& = & 6+12 \\\Leftrightarrow & \color{red}{-143} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-143} & & \\\Leftrightarrow & x = \frac{-18}{143} & & \\ & V = \left\{ \frac{-18}{143} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{8})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -9x-\frac{15}{8}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-72}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -72x \color{red}{-15} & = & \color{red}{56x} +3 \\\Leftrightarrow & -72x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +3 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & -72x-56x& = & 3+15 \\\Leftrightarrow & \color{red}{-128} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-128} & & \\\Leftrightarrow & x = \frac{-9}{64} & & \\ & V = \left\{ \frac{-9}{64} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{7})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{-12} & = & \color{red}{126x} +63 \\\Leftrightarrow & 56x \color{red}{-12} \color{blue}{+12} \color{blue}{-126x} & = & \color{red}{126x} +63 \color{blue}{-126x} \color{blue}{+12} \\\Leftrightarrow & 56x-126x& = & 63+12 \\\Leftrightarrow & \color{red}{-70} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-70} & & \\\Leftrightarrow & x = \frac{-15}{14} & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-70} & = & \color{red}{75x} +6 \\\Leftrightarrow & 315x \color{red}{-70} \color{blue}{+70} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{+70} \\\Leftrightarrow & 315x-75x& = & 6+70 \\\Leftrightarrow & \color{red}{240} x& = & 76 \\\Leftrightarrow & x = \frac{76}{240} & & \\\Leftrightarrow & x = \frac{19}{60} & & \\ & V = \left\{ \frac{19}{60} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{4})& = & 6x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{15}{4}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{120}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{+75} & = & \color{red}{120x} +24 \\\Leftrightarrow & -500x \color{red}{+75} \color{blue}{-75} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{-75} \\\Leftrightarrow & -500x-120x& = & 24-75 \\\Leftrightarrow & \color{red}{-620} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-620} & & \\\Leftrightarrow & x = \frac{51}{620} & & \\ & V = \left\{ \frac{51}{620} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{+35} \\\Leftrightarrow & 84x+30x& = & 9+35 \\\Leftrightarrow & \color{red}{114} x& = & 44 \\\Leftrightarrow & x = \frac{44}{114} & & \\\Leftrightarrow & x = \frac{22}{57} & & \\ & V = \left\{ \frac{22}{57} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{200x} +48 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{-75} \\\Leftrightarrow & 480x-200x& = & 48-75 \\\Leftrightarrow & \color{red}{280} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{280} & & \\ & V = \left\{ \frac{-27}{280} \right\} & \\\end{align}\)