Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x+\frac{24}{11}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3960}{ \color{blue}{132} }x+ \frac{288}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3960x \color{red}{+288} & = & \color{red}{-924x} +55 \\\Leftrightarrow & -3960x \color{red}{+288} \color{blue}{-288} \color{blue}{+924x} & = & \color{red}{-924x} +55 \color{blue}{+924x} \color{blue}{-288} \\\Leftrightarrow & -3960x+924x& = & 55-288 \\\Leftrightarrow & \color{red}{-3036} x& = & -233 \\\Leftrightarrow & x = \frac{-233}{-3036} & & \\\Leftrightarrow & x = \frac{233}{3036} & & \\ & V = \left\{ \frac{233}{3036} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{-224x} +80 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{+224x} & = & \color{red}{-224x} +80 \color{blue}{+224x} \color{blue}{-105} \\\Leftrightarrow & 840x+224x& = & 80-105 \\\Leftrightarrow & \color{red}{1064} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1064} & & \\ & V = \left\{ \frac{-25}{1064} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{105x} +40 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-12} \\\Leftrightarrow & -90x-105x& = & 40-12 \\\Leftrightarrow & \color{red}{-195} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-195} & & \\\Leftrightarrow & x = \frac{-28}{195} & & \\ & V = \left\{ \frac{-28}{195} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{11})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{28}{11}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2310}{ \color{blue}{110} }x+ \frac{280}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2310x \color{red}{+280} & = & \color{red}{-880x} +99 \\\Leftrightarrow & -2310x \color{red}{+280} \color{blue}{-280} \color{blue}{+880x} & = & \color{red}{-880x} +99 \color{blue}{+880x} \color{blue}{-280} \\\Leftrightarrow & -2310x+880x& = & 99-280 \\\Leftrightarrow & \color{red}{-1430} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{-1430} & & \\\Leftrightarrow & x = \frac{181}{1430} & & \\ & V = \left\{ \frac{181}{1430} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +25 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +25 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 25-36 \\\Leftrightarrow & \color{red}{255} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{255} & & \\ & V = \left\{ \frac{-11}{255} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -6x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -6x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-20} & = & \color{red}{-42x} +10 \\\Leftrightarrow & 175x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +10 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & 175x+42x& = & 10+20 \\\Leftrightarrow & \color{red}{217} x& = & 30 \\\Leftrightarrow & x = \frac{30}{217} & & \\ & V = \left\{ \frac{30}{217} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-40} & = & \color{red}{18x} +21 \\\Leftrightarrow & -48x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & -48x-18x& = & 21+40 \\\Leftrightarrow & \color{red}{-66} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-66} & & \\\Leftrightarrow & x = \frac{-61}{66} & & \\ & V = \left\{ \frac{-61}{66} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{8})& = & 8x+\frac{8}{11} \\\Leftrightarrow & 35x-\frac{35}{8}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-385} & = & \color{red}{704x} +64 \\\Leftrightarrow & 3080x \color{red}{-385} \color{blue}{+385} \color{blue}{-704x} & = & \color{red}{704x} +64 \color{blue}{-704x} \color{blue}{+385} \\\Leftrightarrow & 3080x-704x& = & 64+385 \\\Leftrightarrow & \color{red}{2376} x& = & 449 \\\Leftrightarrow & x = \frac{449}{2376} & & \\ & V = \left\{ \frac{449}{2376} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{4})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{35}{4}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{700}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 700x \color{red}{-175} & = & \color{red}{60x} +24 \\\Leftrightarrow & 700x \color{red}{-175} \color{blue}{+175} \color{blue}{-60x} & = & \color{red}{60x} +24 \color{blue}{-60x} \color{blue}{+175} \\\Leftrightarrow & 700x-60x& = & 24+175 \\\Leftrightarrow & \color{red}{640} x& = & 199 \\\Leftrightarrow & x = \frac{199}{640} & & \\ & V = \left\{ \frac{199}{640} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{27x} +2 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+14} \\\Leftrightarrow & 105x-27x& = & 2+14 \\\Leftrightarrow & \color{red}{78} x& = & 16 \\\Leftrightarrow & x = \frac{16}{78} & & \\\Leftrightarrow & x = \frac{8}{39} & & \\ & V = \left\{ \frac{8}{39} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{15}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+45} & = & \color{red}{99x} +88 \\\Leftrightarrow & -660x \color{red}{+45} \color{blue}{-45} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{-45} \\\Leftrightarrow & -660x-99x& = & 88-45 \\\Leftrightarrow & \color{red}{-759} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-759} & & \\\Leftrightarrow & x = \frac{-43}{759} & & \\ & V = \left\{ \frac{-43}{759} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-6} & = & \color{red}{-35x} +9 \\\Leftrightarrow & 84x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & 84x+35x& = & 9+6 \\\Leftrightarrow & \color{red}{119} x& = & 15 \\\Leftrightarrow & x = \frac{15}{119} & & \\ & V = \left\{ \frac{15}{119} \right\} & \\\end{align}\)