Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{-40x} +14 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{+40x} & = & \color{red}{-40x} +14 \color{blue}{+40x} \color{blue}{-21} \\\Leftrightarrow & 168x+40x& = & 14-21 \\\Leftrightarrow & \color{red}{208} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{208} & & \\ & V = \left\{ \frac{-7}{208} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+66} & = & \color{red}{165x} +50 \\\Leftrightarrow & 440x \color{red}{+66} \color{blue}{-66} \color{blue}{-165x} & = & \color{red}{165x} +50 \color{blue}{-165x} \color{blue}{-66} \\\Leftrightarrow & 440x-165x& = & 50-66 \\\Leftrightarrow & \color{red}{275} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{275} & & \\ & V = \left\{ \frac{-16}{275} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{12}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-12} & = & \color{red}{35x} +2 \\\Leftrightarrow & 42x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 42x-35x& = & 2+12 \\\Leftrightarrow & \color{red}{7} x& = & 14 \\\Leftrightarrow & x = \frac{14}{7} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{10}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+10} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 180x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & 180x+63x& = & 30-10 \\\Leftrightarrow & \color{red}{243} x& = & 20 \\\Leftrightarrow & x = \frac{20}{243} & & \\ & V = \left\{ \frac{20}{243} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{11})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{20}{11}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-140} & = & \color{red}{693x} +110 \\\Leftrightarrow & 1540x \color{red}{-140} \color{blue}{+140} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+140} \\\Leftrightarrow & 1540x-693x& = & 110+140 \\\Leftrightarrow & \color{red}{847} x& = & 250 \\\Leftrightarrow & x = \frac{250}{847} & & \\ & V = \left\{ \frac{250}{847} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{30x} +25 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{-30x} & = & \color{red}{30x} +25 \color{blue}{-30x} \color{blue}{+24} \\\Leftrightarrow & -80x-30x& = & 25+24 \\\Leftrightarrow & \color{red}{-110} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-110} & & \\\Leftrightarrow & x = \frac{-49}{110} & & \\ & V = \left\{ \frac{-49}{110} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x- \frac{40}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{-210x} +21 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{+40} \\\Leftrightarrow & -300x+210x& = & 21+40 \\\Leftrightarrow & \color{red}{-90} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-90} & & \\\Leftrightarrow & x = \frac{-61}{90} & & \\ & V = \left\{ \frac{-61}{90} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & 3x+\frac{7}{4} \\\Leftrightarrow & -35x-\frac{35}{8}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{35}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-35} & = & \color{red}{24x} +14 \\\Leftrightarrow & -280x \color{red}{-35} \color{blue}{+35} \color{blue}{-24x} & = & \color{red}{24x} +14 \color{blue}{-24x} \color{blue}{+35} \\\Leftrightarrow & -280x-24x& = & 14+35 \\\Leftrightarrow & \color{red}{-304} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-304} & & \\\Leftrightarrow & x = \frac{-49}{304} & & \\ & V = \left\{ \frac{-49}{304} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -6x+\frac{8}{11} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -6x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+110} & = & \color{red}{-462x} +56 \\\Leftrightarrow & 1925x \color{red}{+110} \color{blue}{-110} \color{blue}{+462x} & = & \color{red}{-462x} +56 \color{blue}{+462x} \color{blue}{-110} \\\Leftrightarrow & 1925x+462x& = & 56-110 \\\Leftrightarrow & \color{red}{2387} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{2387} & & \\ & V = \left\{ \frac{-54}{2387} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{6})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 28x+\frac{35}{6}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{150x} +24 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{-150x} & = & \color{red}{150x} +24 \color{blue}{-150x} \color{blue}{-175} \\\Leftrightarrow & 840x-150x& = & 24-175 \\\Leftrightarrow & \color{red}{690} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{690} & & \\ & V = \left\{ \frac{-151}{690} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -9x+\frac{9}{10} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{-60} & = & \color{red}{-630x} +63 \\\Leftrightarrow & 560x \color{red}{-60} \color{blue}{+60} \color{blue}{+630x} & = & \color{red}{-630x} +63 \color{blue}{+630x} \color{blue}{+60} \\\Leftrightarrow & 560x+630x& = & 63+60 \\\Leftrightarrow & \color{red}{1190} x& = & 123 \\\Leftrightarrow & x = \frac{123}{1190} & & \\ & V = \left\{ \frac{123}{1190} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & 6x+\frac{6}{11} \\\Leftrightarrow & 25x+\frac{15}{11}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{+15} & = & \color{red}{66x} +6 \\\Leftrightarrow & 275x \color{red}{+15} \color{blue}{-15} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{-15} \\\Leftrightarrow & 275x-66x& = & 6-15 \\\Leftrightarrow & \color{red}{209} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{209} & & \\ & V = \left\{ \frac{-9}{209} \right\} & \\\end{align}\)