Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{+42} \\\Leftrightarrow & 210x+175x& = & 40+42 \\\Leftrightarrow & \color{red}{385} x& = & 82 \\\Leftrightarrow & x = \frac{82}{385} & & \\ & V = \left\{ \frac{82}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 4x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{132x} +6 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{-132x} & = & \color{red}{132x} +6 \color{blue}{-132x} \color{blue}{-220} \\\Leftrightarrow & 495x-132x& = & 6-220 \\\Leftrightarrow & \color{red}{363} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{363} & & \\ & V = \left\{ \frac{-214}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{6})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -28x-\frac{35}{6}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1176}{ \color{blue}{42} }x- \frac{245}{ \color{blue}{42} })& = & (\frac{-336}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1176x \color{red}{-245} & = & \color{red}{-336x} +60 \\\Leftrightarrow & -1176x \color{red}{-245} \color{blue}{+245} \color{blue}{+336x} & = & \color{red}{-336x} +60 \color{blue}{+336x} \color{blue}{+245} \\\Leftrightarrow & -1176x+336x& = & 60+245 \\\Leftrightarrow & \color{red}{-840} x& = & 305 \\\Leftrightarrow & x = \frac{305}{-840} & & \\\Leftrightarrow & x = \frac{-61}{168} & & \\ & V = \left\{ \frac{-61}{168} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & -8x+\frac{5}{11} \\\Leftrightarrow & 35x+\frac{35}{3}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+385} & = & \color{red}{-264x} +15 \\\Leftrightarrow & 1155x \color{red}{+385} \color{blue}{-385} \color{blue}{+264x} & = & \color{red}{-264x} +15 \color{blue}{+264x} \color{blue}{-385} \\\Leftrightarrow & 1155x+264x& = & 15-385 \\\Leftrightarrow & \color{red}{1419} x& = & -370 \\\Leftrightarrow & x = \frac{-370}{1419} & & \\ & V = \left\{ \frac{-370}{1419} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & 6x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 6x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{30}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{30x} +2 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-30x} & = & \color{red}{30x} +2 \color{blue}{-30x} \color{blue}{-12} \\\Leftrightarrow & -90x-30x& = & 2-12 \\\Leftrightarrow & \color{red}{-120} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-120} & & \\\Leftrightarrow & x = \frac{1}{12} & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 8x+\frac{8}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{245x} +63 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-40} \\\Leftrightarrow & 280x-245x& = & 63-40 \\\Leftrightarrow & \color{red}{35} x& = & 23 \\\Leftrightarrow & x = \frac{23}{35} & & \\ & V = \left\{ \frac{23}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & -6x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{35}{9}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{-594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-385} & = & \color{red}{-594x} +54 \\\Leftrightarrow & -3465x \color{red}{-385} \color{blue}{+385} \color{blue}{+594x} & = & \color{red}{-594x} +54 \color{blue}{+594x} \color{blue}{+385} \\\Leftrightarrow & -3465x+594x& = & 54+385 \\\Leftrightarrow & \color{red}{-2871} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-2871} & & \\\Leftrightarrow & x = \frac{-439}{2871} & & \\ & V = \left\{ \frac{-439}{2871} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{-84x} +32 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +32 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & 72x+84x& = & 32+45 \\\Leftrightarrow & \color{red}{156} x& = & 77 \\\Leftrightarrow & x = \frac{77}{156} & & \\ & V = \left\{ \frac{77}{156} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 2x+\frac{9}{7} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 2x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{56x} +36 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{-56x} & = & \color{red}{56x} +36 \color{blue}{-56x} \color{blue}{+105} \\\Leftrightarrow & 252x-56x& = & 36+105 \\\Leftrightarrow & \color{red}{196} x& = & 141 \\\Leftrightarrow & x = \frac{141}{196} & & \\ & V = \left\{ \frac{141}{196} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{4}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+12} & = & \color{red}{297x} +88 \\\Leftrightarrow & -132x \color{red}{+12} \color{blue}{-12} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{-12} \\\Leftrightarrow & -132x-297x& = & 88-12 \\\Leftrightarrow & \color{red}{-429} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-429} & & \\\Leftrightarrow & x = \frac{-76}{429} & & \\ & V = \left\{ \frac{-76}{429} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-66} & = & \color{red}{-539x} +21 \\\Leftrightarrow & -770x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +21 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -770x+539x& = & 21+66 \\\Leftrightarrow & \color{red}{-231} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-231} & & \\\Leftrightarrow & x = \frac{-29}{77} & & \\ & V = \left\{ \frac{-29}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{16}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-16} & = & \color{red}{-9x} +10 \\\Leftrightarrow & 60x \color{red}{-16} \color{blue}{+16} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+16} \\\Leftrightarrow & 60x+9x& = & 10+16 \\\Leftrightarrow & \color{red}{69} x& = & 26 \\\Leftrightarrow & x = \frac{26}{69} & & \\ & V = \left\{ \frac{26}{69} \right\} & \\\end{align}\)