Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & 3x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 6 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{36x} +5 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{-36x} & = & \color{red}{36x} +5 \color{blue}{-36x} \color{blue}{+50} \\\Leftrightarrow & 120x-36x& = & 5+50 \\\Leftrightarrow & \color{red}{84} x& = & 55 \\\Leftrightarrow & x = \frac{55}{84} & & \\ & V = \left\{ \frac{55}{84} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{120x} +10 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{-36} \\\Leftrightarrow & 225x-120x& = & 10-36 \\\Leftrightarrow & \color{red}{105} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{105} & & \\ & V = \left\{ \frac{-26}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 100x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & 100x+35x& = & 6-12 \\\Leftrightarrow & \color{red}{135} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{135} & & \\\Leftrightarrow & x = \frac{-2}{45} & & \\ & V = \left\{ \frac{-2}{45} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{5})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{16}{5}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x+ \frac{16}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{+16} & = & \color{red}{-45x} +2 \\\Leftrightarrow & -100x \color{red}{+16} \color{blue}{-16} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{-16} \\\Leftrightarrow & -100x+45x& = & 2-16 \\\Leftrightarrow & \color{red}{-55} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-55} & & \\\Leftrightarrow & x = \frac{14}{55} & & \\ & V = \left\{ \frac{14}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{7}{5} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{125}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+125} & = & \color{red}{-135x} +63 \\\Leftrightarrow & -900x \color{red}{+125} \color{blue}{-125} \color{blue}{+135x} & = & \color{red}{-135x} +63 \color{blue}{+135x} \color{blue}{-125} \\\Leftrightarrow & -900x+135x& = & 63-125 \\\Leftrightarrow & \color{red}{-765} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-765} & & \\\Leftrightarrow & x = \frac{62}{765} & & \\ & V = \left\{ \frac{62}{765} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{+32} & = & \color{red}{60x} +21 \\\Leftrightarrow & 144x \color{red}{+32} \color{blue}{-32} \color{blue}{-60x} & = & \color{red}{60x} +21 \color{blue}{-60x} \color{blue}{-32} \\\Leftrightarrow & 144x-60x& = & 21-32 \\\Leftrightarrow & \color{red}{84} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{84} & & \\ & V = \left\{ \frac{-11}{84} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{8}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-8} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 36x \color{red}{-8} \color{blue}{+8} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+8} \\\Leftrightarrow & 36x+15x& = & 8+8 \\\Leftrightarrow & \color{red}{51} x& = & 16 \\\Leftrightarrow & x = \frac{16}{51} & & \\ & V = \left\{ \frac{16}{51} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{7})& = & 4x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{9}{7}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-99} & = & \color{red}{308x} +70 \\\Leftrightarrow & 1155x \color{red}{-99} \color{blue}{+99} \color{blue}{-308x} & = & \color{red}{308x} +70 \color{blue}{-308x} \color{blue}{+99} \\\Leftrightarrow & 1155x-308x& = & 70+99 \\\Leftrightarrow & \color{red}{847} x& = & 169 \\\Leftrightarrow & x = \frac{169}{847} & & \\ & V = \left\{ \frac{169}{847} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{12}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+12} & = & \color{red}{-77x} +6 \\\Leftrightarrow & 88x \color{red}{+12} \color{blue}{-12} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-12} \\\Leftrightarrow & 88x+77x& = & 6-12 \\\Leftrightarrow & \color{red}{165} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{165} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{11})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{10}{11}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+30} & = & \color{red}{-66x} +88 \\\Leftrightarrow & 495x \color{red}{+30} \color{blue}{-30} \color{blue}{+66x} & = & \color{red}{-66x} +88 \color{blue}{+66x} \color{blue}{-30} \\\Leftrightarrow & 495x+66x& = & 88-30 \\\Leftrightarrow & \color{red}{561} x& = & 58 \\\Leftrightarrow & x = \frac{58}{561} & & \\ & V = \left\{ \frac{58}{561} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 540x+225x& = & 40+108 \\\Leftrightarrow & \color{red}{765} x& = & 148 \\\Leftrightarrow & x = \frac{148}{765} & & \\ & V = \left\{ \frac{148}{765} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -30x-\frac{24}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{-48} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -300x \color{red}{-48} \color{blue}{+48} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+48} \\\Leftrightarrow & -300x+70x& = & 15+48 \\\Leftrightarrow & \color{red}{-230} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-230} & & \\\Leftrightarrow & x = \frac{-63}{230} & & \\ & V = \left\{ \frac{-63}{230} \right\} & \\\end{align}\)