Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(3(-4x-\frac{4}{5})=5x+\frac{2}{15}\)
2. \((5x-\frac{3}{7})=6x+\frac{2}{5}\)
3. \(-4(x-\frac{5}{6})=7x+\frac{4}{13}\)
4. \(-2(x-\frac{3}{13})=7x+\frac{6}{11}\)
5. \((-3x+\frac{4}{3})=-5x+\frac{5}{4}\)
6. \(-(3x+\frac{5}{7})=8x+\frac{7}{12}\)
7. \((-x-\frac{3}{16})=-9x+\frac{2}{9}\)
8. \(2(4x+\frac{5}{12})=7x+\frac{2}{9}\)
9. \(-2(x-\frac{2}{7})=5x+\frac{6}{5}\)
10. \(-7(-4x-\frac{2}{13})=5x+\frac{5}{2}\)
11. \(4(-x-\frac{3}{7})=7x+\frac{9}{16}\)
12. \((3x-\frac{5}{12})=-5x+\frac{3}{8}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{2}{15} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{2}{15} \\ & & & \text{kgv van noemers 5 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(-12x-\frac{12}{5})& = & (5x+\frac{2}{15}). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +2 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +2 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 2+36 \\\Leftrightarrow & \color{red}{-255} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-255} & & \\\Leftrightarrow & x = \frac{-38}{255} & & \\ & V = \left\{ \frac{-38}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (5x-\frac{3}{7})& = & 6x+\frac{2}{5} \\\Leftrightarrow & 5x-\frac{3}{7}& = & 6x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(5x-\frac{3}{7})& = & (6x+\frac{2}{5}). \color{blue}{35} \\\Leftrightarrow & 175x \color{red}{-15} & = & \color{red}{210x} +14 \\\Leftrightarrow & 175x \color{red}{-15} \color{blue}{+15} \color{blue}{-210x} & = & \color{red}{210x} +14 \color{blue}{-210x} \color{blue}{+15} \\\Leftrightarrow & 175x-210x& = & 14+15 \\\Leftrightarrow & \color{red}{-35} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-35} & & \\\Leftrightarrow & x = \frac{-29}{35} & & \\ & V = \left\{ \frac{-29}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (x-\frac{5}{6})& = & 7x+\frac{4}{13} \\\Leftrightarrow & -4x+\frac{10}{3}& = & 7x+\frac{4}{13} \\ & & & \text{kgv van noemers 3 en 13 is 39} \\\Leftrightarrow & \color{blue}{39} .(-4x+\frac{10}{3})& = & (7x+\frac{4}{13}). \color{blue}{39} \\\Leftrightarrow & -156x \color{red}{+130} & = & \color{red}{273x} +12 \\\Leftrightarrow & -156x \color{red}{+130} \color{blue}{-130} \color{blue}{-273x} & = & \color{red}{273x} +12 \color{blue}{-273x} \color{blue}{-130} \\\Leftrightarrow & -156x-273x& = & 12-130 \\\Leftrightarrow & \color{red}{-429} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-429} & & \\\Leftrightarrow & x = \frac{118}{429} & & \\ & V = \left\{ \frac{118}{429} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (x-\frac{3}{13})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -2x+\frac{6}{13}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 13 en 11 is 143} \\\Leftrightarrow & \color{blue}{143} .(-2x+\frac{6}{13})& = & (7x+\frac{6}{11}). \color{blue}{143} \\\Leftrightarrow & -286x \color{red}{+66} & = & \color{red}{1001x} +78 \\\Leftrightarrow & -286x \color{red}{+66} \color{blue}{-66} \color{blue}{-1001x} & = & \color{red}{1001x} +78 \color{blue}{-1001x} \color{blue}{-66} \\\Leftrightarrow & -286x-1001x& = & 78-66 \\\Leftrightarrow & \color{red}{-1287} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-1287} & & \\\Leftrightarrow & x = \frac{-4}{429} & & \\ & V = \left\{ \frac{-4}{429} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-3x+\frac{4}{3})& = & -5x+\frac{5}{4} \\\Leftrightarrow & -3x+\frac{4}{3}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(-3x+\frac{4}{3})& = & (-5x+\frac{5}{4}). \color{blue}{12} \\\Leftrightarrow & -36x \color{red}{+16} & = & \color{red}{-60x} +15 \\\Leftrightarrow & -36x \color{red}{+16} \color{blue}{-16} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{-16} \\\Leftrightarrow & -36x+60x& = & 15-16 \\\Leftrightarrow & \color{red}{24} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{24} & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (3x+\frac{5}{7})& = & 8x+\frac{7}{12} \\\Leftrightarrow & -3x-\frac{5}{7}& = & 8x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(-3x-\frac{5}{7})& = & (8x+\frac{7}{12}). \color{blue}{84} \\\Leftrightarrow & -252x \color{red}{-60} & = & \color{red}{672x} +49 \\\Leftrightarrow & -252x \color{red}{-60} \color{blue}{+60} \color{blue}{-672x} & = & \color{red}{672x} +49 \color{blue}{-672x} \color{blue}{+60} \\\Leftrightarrow & -252x-672x& = & 49+60 \\\Leftrightarrow & \color{red}{-924} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-924} & & \\\Leftrightarrow & x = \frac{-109}{924} & & \\ & V = \left\{ \frac{-109}{924} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-x-\frac{3}{16})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -x-\frac{3}{16}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 16 en 9 is 144} \\\Leftrightarrow & \color{blue}{144} .(-x-\frac{3}{16})& = & (-9x+\frac{2}{9}). \color{blue}{144} \\\Leftrightarrow & -144x \color{red}{-27} & = & \color{red}{-1296x} +32 \\\Leftrightarrow & -144x \color{red}{-27} \color{blue}{+27} \color{blue}{+1296x} & = & \color{red}{-1296x} +32 \color{blue}{+1296x} \color{blue}{+27} \\\Leftrightarrow & -144x+1296x& = & 32+27 \\\Leftrightarrow & \color{red}{1152} x& = & 59 \\\Leftrightarrow & x = \frac{59}{1152} & & \\ & V = \left\{ \frac{59}{1152} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{12})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 8x+\frac{5}{6}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(8x+\frac{5}{6})& = & (7x+\frac{2}{9}). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+15} & = & \color{red}{126x} +4 \\\Leftrightarrow & 144x \color{red}{+15} \color{blue}{-15} \color{blue}{-126x} & = & \color{red}{126x} +4 \color{blue}{-126x} \color{blue}{-15} \\\Leftrightarrow & 144x-126x& = & 4-15 \\\Leftrightarrow & \color{red}{18} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{18} & & \\ & V = \left\{ \frac{-11}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (x-\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -2x+\frac{4}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(-2x+\frac{4}{7})& = & (5x+\frac{6}{5}). \color{blue}{35} \\\Leftrightarrow & -70x \color{red}{+20} & = & \color{red}{175x} +42 \\\Leftrightarrow & -70x \color{red}{+20} \color{blue}{-20} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-20} \\\Leftrightarrow & -70x-175x& = & 42-20 \\\Leftrightarrow & \color{red}{-245} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-245} & & \\\Leftrightarrow & x = \frac{-22}{245} & & \\ & V = \left\{ \frac{-22}{245} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{13})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{14}{13}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 13 en 2 is 26} \\\Leftrightarrow & \color{blue}{26} .(28x+\frac{14}{13})& = & (5x+\frac{5}{2}). \color{blue}{26} \\\Leftrightarrow & 728x \color{red}{+28} & = & \color{red}{130x} +65 \\\Leftrightarrow & 728x \color{red}{+28} \color{blue}{-28} \color{blue}{-130x} & = & \color{red}{130x} +65 \color{blue}{-130x} \color{blue}{-28} \\\Leftrightarrow & 728x-130x& = & 65-28 \\\Leftrightarrow & \color{red}{598} x& = & 37 \\\Leftrightarrow & x = \frac{37}{598} & & \\ & V = \left\{ \frac{37}{598} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-x-\frac{3}{7})& = & 7x+\frac{9}{16} \\\Leftrightarrow & -4x-\frac{12}{7}& = & 7x+\frac{9}{16} \\ & & & \text{kgv van noemers 7 en 16 is 112} \\\Leftrightarrow & \color{blue}{112} .(-4x-\frac{12}{7})& = & (7x+\frac{9}{16}). \color{blue}{112} \\\Leftrightarrow & -448x \color{red}{-192} & = & \color{red}{784x} +63 \\\Leftrightarrow & -448x \color{red}{-192} \color{blue}{+192} \color{blue}{-784x} & = & \color{red}{784x} +63 \color{blue}{-784x} \color{blue}{+192} \\\Leftrightarrow & -448x-784x& = & 63+192 \\\Leftrightarrow & \color{red}{-1232} x& = & 255 \\\Leftrightarrow & x = \frac{255}{-1232} & & \\\Leftrightarrow & x = \frac{-255}{1232} & & \\ & V = \left\{ \frac{-255}{1232} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (3x-\frac{5}{12})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 3x-\frac{5}{12}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(3x-\frac{5}{12})& = & (-5x+\frac{3}{8}). \color{blue}{24} \\\Leftrightarrow & 72x \color{red}{-10} & = & \color{red}{-120x} +9 \\\Leftrightarrow & 72x \color{red}{-10} \color{blue}{+10} \color{blue}{+120x} & = & \color{red}{-120x} +9 \color{blue}{+120x} \color{blue}{+10} \\\Leftrightarrow & 72x+120x& = & 9+10 \\\Leftrightarrow & \color{red}{192} x& = & 19 \\\Leftrightarrow & x = \frac{19}{192} & & \\ & V = \left\{ \frac{19}{192} \right\} & \\\end{align}\)