Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{9})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -12x+\frac{16}{9}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1080}{ \color{blue}{90} }x+ \frac{160}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1080x \color{red}{+160} & = & \color{red}{-450x} +63 \\\Leftrightarrow & -1080x \color{red}{+160} \color{blue}{-160} \color{blue}{+450x} & = & \color{red}{-450x} +63 \color{blue}{+450x} \color{blue}{-160} \\\Leftrightarrow & -1080x+450x& = & 63-160 \\\Leftrightarrow & \color{red}{-630} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-630} & & \\\Leftrightarrow & x = \frac{97}{630} & & \\ & V = \left\{ \frac{97}{630} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{8}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+8} & = & \color{red}{35x} +6 \\\Leftrightarrow & 100x \color{red}{+8} \color{blue}{-8} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-8} \\\Leftrightarrow & 100x-35x& = & 6-8 \\\Leftrightarrow & \color{red}{65} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{65} & & \\ & V = \left\{ \frac{-2}{65} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{5})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{-135x} +40 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-108} \\\Leftrightarrow & 900x+135x& = & 40-108 \\\Leftrightarrow & \color{red}{1035} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1035} & & \\ & V = \left\{ \frac{-68}{1035} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{16}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-16} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -60x \color{red}{-16} \color{blue}{+16} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{+16} \\\Leftrightarrow & -60x+21x& = & 8+16 \\\Leftrightarrow & \color{red}{-39} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-39} & & \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-24} & = & \color{red}{-30x} +15 \\\Leftrightarrow & -180x \color{red}{-24} \color{blue}{+24} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{+24} \\\Leftrightarrow & -180x+30x& = & 15+24 \\\Leftrightarrow & \color{red}{-150} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-150} & & \\\Leftrightarrow & x = \frac{-13}{50} & & \\ & V = \left\{ \frac{-13}{50} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & 630x+441x& = & 14-90 \\\Leftrightarrow & \color{red}{1071} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{1071} & & \\ & V = \left\{ \frac{-76}{1071} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{9}{5}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+9} & = & \color{red}{-20x} +6 \\\Leftrightarrow & -75x \color{red}{+9} \color{blue}{-9} \color{blue}{+20x} & = & \color{red}{-20x} +6 \color{blue}{+20x} \color{blue}{-9} \\\Leftrightarrow & -75x+20x& = & 6-9 \\\Leftrightarrow & \color{red}{-55} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-55} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+14} & = & \color{red}{-24x} +8 \\\Leftrightarrow & 63x \color{red}{+14} \color{blue}{-14} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{-14} \\\Leftrightarrow & 63x+24x& = & 8-14 \\\Leftrightarrow & \color{red}{87} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{87} & & \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{-8} \\\Leftrightarrow & -60x+70x& = & 25-8 \\\Leftrightarrow & \color{red}{10} x& = & 17 \\\Leftrightarrow & x = \frac{17}{10} & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & 504x+441x& = & 14+54 \\\Leftrightarrow & \color{red}{945} x& = & 68 \\\Leftrightarrow & x = \frac{68}{945} & & \\ & V = \left\{ \frac{68}{945} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{9})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{20}{9}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+20} & = & \color{red}{18x} +30 \\\Leftrightarrow & 225x \color{red}{+20} \color{blue}{-20} \color{blue}{-18x} & = & \color{red}{18x} +30 \color{blue}{-18x} \color{blue}{-20} \\\Leftrightarrow & 225x-18x& = & 30-20 \\\Leftrightarrow & \color{red}{207} x& = & 10 \\\Leftrightarrow & x = \frac{10}{207} & & \\ & V = \left\{ \frac{10}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{9})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{16}{9}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{32}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-32} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -216x \color{red}{-32} \color{blue}{+32} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+32} \\\Leftrightarrow & -216x+90x& = & 45+32 \\\Leftrightarrow & \color{red}{-126} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-126} & & \\\Leftrightarrow & x = \frac{-11}{18} & & \\ & V = \left\{ \frac{-11}{18} \right\} & \\\end{align}\)