Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{7})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{-24} & = & \color{red}{84x} +35 \\\Leftrightarrow & 112x \color{red}{-24} \color{blue}{+24} \color{blue}{-84x} & = & \color{red}{84x} +35 \color{blue}{-84x} \color{blue}{+24} \\\Leftrightarrow & 112x-84x& = & 35+24 \\\Leftrightarrow & \color{red}{28} x& = & 59 \\\Leftrightarrow & x = \frac{59}{28} & & \\ & V = \left\{ \frac{59}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{405x} +54 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{-405x} & = & \color{red}{405x} +54 \color{blue}{-405x} \color{blue}{+140} \\\Leftrightarrow & 630x-405x& = & 54+140 \\\Leftrightarrow & \color{red}{225} x& = & 194 \\\Leftrightarrow & x = \frac{194}{225} & & \\ & V = \left\{ \frac{194}{225} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-110} & = & \color{red}{-693x} +42 \\\Leftrightarrow & -1540x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -1540x+693x& = & 42+110 \\\Leftrightarrow & \color{red}{-847} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-847} & & \\\Leftrightarrow & x = \frac{-152}{847} & & \\ & V = \left\{ \frac{-152}{847} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{4}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-4} & = & \color{red}{-21x} +2 \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+4} \\\Leftrightarrow & 24x+21x& = & 2+4 \\\Leftrightarrow & \color{red}{45} x& = & 6 \\\Leftrightarrow & x = \frac{6}{45} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-180} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 504x \color{red}{-180} \color{blue}{+180} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+180} \\\Leftrightarrow & 504x+315x& = & 14+180 \\\Leftrightarrow & \color{red}{819} x& = & 194 \\\Leftrightarrow & x = \frac{194}{819} & & \\ & V = \left\{ \frac{194}{819} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{11})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 25x+\frac{10}{11}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2200}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2200x \color{red}{+80} & = & \color{red}{-264x} +77 \\\Leftrightarrow & 2200x \color{red}{+80} \color{blue}{-80} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{-80} \\\Leftrightarrow & 2200x+264x& = & 77-80 \\\Leftrightarrow & \color{red}{2464} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{2464} & & \\ & V = \left\{ \frac{-3}{2464} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{1}{2})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{5}{2}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{40}{ \color{blue}{2} }x- \frac{5}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 40x \color{red}{-5} & = & \color{red}{-14x} +3 \\\Leftrightarrow & 40x \color{red}{-5} \color{blue}{+5} \color{blue}{+14x} & = & \color{red}{-14x} +3 \color{blue}{+14x} \color{blue}{+5} \\\Leftrightarrow & 40x+14x& = & 3+5 \\\Leftrightarrow & \color{red}{54} x& = & 8 \\\Leftrightarrow & x = \frac{8}{54} & & \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & -180x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{-105} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-105} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+40} & = & \color{red}{-42x} +15 \\\Leftrightarrow & -60x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & -60x+42x& = & 15-40 \\\Leftrightarrow & \color{red}{-18} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-18} & & \\\Leftrightarrow & x = \frac{25}{18} & & \\ & V = \left\{ \frac{25}{18} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 60x+25x& = & 4-12 \\\Leftrightarrow & \color{red}{85} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{85} & & \\ & V = \left\{ \frac{-8}{85} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{8}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-24} & = & \color{red}{105x} +20 \\\Leftrightarrow & -300x \color{red}{-24} \color{blue}{+24} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+24} \\\Leftrightarrow & -300x-105x& = & 20+24 \\\Leftrightarrow & \color{red}{-405} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-405} & & \\\Leftrightarrow & x = \frac{-44}{405} & & \\ & V = \left\{ \frac{-44}{405} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-42} & = & \color{red}{245x} +45 \\\Leftrightarrow & -350x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & -350x-245x& = & 45+42 \\\Leftrightarrow & \color{red}{-595} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-595} & & \\\Leftrightarrow & x = \frac{-87}{595} & & \\ & V = \left\{ \frac{-87}{595} \right\} & \\\end{align}\)