Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{9})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{10}{9}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{126x} +63 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{-126x} & = & \color{red}{126x} +63 \color{blue}{-126x} \color{blue}{-20} \\\Leftrightarrow & 180x-126x& = & 63-20 \\\Leftrightarrow & \color{red}{54} x& = & 43 \\\Leftrightarrow & x = \frac{43}{54} & & \\ & V = \left\{ \frac{43}{54} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{7})& = & 7x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{245x} +21 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-245x} & = & \color{red}{245x} +21 \color{blue}{-245x} \color{blue}{-60} \\\Leftrightarrow & 420x-245x& = & 21-60 \\\Leftrightarrow & \color{red}{175} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{175} & & \\ & V = \left\{ \frac{-39}{175} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{35}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{18x} +21 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+70} \\\Leftrightarrow & -210x-18x& = & 21+70 \\\Leftrightarrow & \color{red}{-228} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-228} & & \\\Leftrightarrow & x = \frac{-91}{228} & & \\ & V = \left\{ \frac{-91}{228} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{2})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -25x-\frac{25}{2}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x- \frac{50}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{-50} & = & \color{red}{-20x} +7 \\\Leftrightarrow & -100x \color{red}{-50} \color{blue}{+50} \color{blue}{+20x} & = & \color{red}{-20x} +7 \color{blue}{+20x} \color{blue}{+50} \\\Leftrightarrow & -100x+20x& = & 7+50 \\\Leftrightarrow & \color{red}{-80} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-80} & & \\\Leftrightarrow & x = \frac{-57}{80} & & \\ & V = \left\{ \frac{-57}{80} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{-49x} +3 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{+30} \\\Leftrightarrow & 210x+49x& = & 3+30 \\\Leftrightarrow & \color{red}{259} x& = & 33 \\\Leftrightarrow & x = \frac{33}{259} & & \\ & V = \left\{ \frac{33}{259} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-24} & = & \color{red}{-70x} +9 \\\Leftrightarrow & -60x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & -60x+70x& = & 9+24 \\\Leftrightarrow & \color{red}{10} x& = & 33 \\\Leftrightarrow & x = \frac{33}{10} & & \\ & V = \left\{ \frac{33}{10} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{25}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{125}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+125} & = & \color{red}{105x} +28 \\\Leftrightarrow & 700x \color{red}{+125} \color{blue}{-125} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-125} \\\Leftrightarrow & 700x-105x& = & 28-125 \\\Leftrightarrow & \color{red}{595} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{595} & & \\ & V = \left\{ \frac{-97}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{9}{10}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+27} & = & \color{red}{150x} +80 \\\Leftrightarrow & -360x \color{red}{+27} \color{blue}{-27} \color{blue}{-150x} & = & \color{red}{150x} +80 \color{blue}{-150x} \color{blue}{-27} \\\Leftrightarrow & -360x-150x& = & 80-27 \\\Leftrightarrow & \color{red}{-510} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-510} & & \\\Leftrightarrow & x = \frac{-53}{510} & & \\ & V = \left\{ \frac{-53}{510} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -54x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -54x+63x& = & 6-8 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2100}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2100x \color{red}{-300} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -2100x \color{red}{-300} \color{blue}{+300} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{+300} \\\Leftrightarrow & -2100x+490x& = & 63+300 \\\Leftrightarrow & \color{red}{-1610} x& = & 363 \\\Leftrightarrow & x = \frac{363}{-1610} & & \\\Leftrightarrow & x = \frac{-363}{1610} & & \\ & V = \left\{ \frac{-363}{1610} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{4}{9}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+28} & = & \color{red}{-441x} +27 \\\Leftrightarrow & 504x \color{red}{+28} \color{blue}{-28} \color{blue}{+441x} & = & \color{red}{-441x} +27 \color{blue}{+441x} \color{blue}{-28} \\\Leftrightarrow & 504x+441x& = & 27-28 \\\Leftrightarrow & \color{red}{945} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{945} & & \\ & V = \left\{ \frac{-1}{945} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{9})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{10}{9}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-10} & = & \color{red}{-27x} +30 \\\Leftrightarrow & 90x \color{red}{-10} \color{blue}{+10} \color{blue}{+27x} & = & \color{red}{-27x} +30 \color{blue}{+27x} \color{blue}{+10} \\\Leftrightarrow & 90x+27x& = & 30+10 \\\Leftrightarrow & \color{red}{117} x& = & 40 \\\Leftrightarrow & x = \frac{40}{117} & & \\ & V = \left\{ \frac{40}{117} \right\} & \\\end{align}\)