Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{+24} & = & \color{red}{-50x} +7 \\\Leftrightarrow & 240x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +7 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 240x+50x& = & 7-24 \\\Leftrightarrow & \color{red}{290} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{290} & & \\ & V = \left\{ \frac{-17}{290} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+72} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{+72} \color{blue}{-72} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{-72} \\\Leftrightarrow & -396x-165x& = & 22-72 \\\Leftrightarrow & \color{red}{-561} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-561} & & \\\Leftrightarrow & x = \frac{50}{561} & & \\ & V = \left\{ \frac{50}{561} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{864}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 864x \color{red}{-64} & = & \color{red}{-504x} +27 \\\Leftrightarrow & 864x \color{red}{-64} \color{blue}{+64} \color{blue}{+504x} & = & \color{red}{-504x} +27 \color{blue}{+504x} \color{blue}{+64} \\\Leftrightarrow & 864x+504x& = & 27+64 \\\Leftrightarrow & \color{red}{1368} x& = & 91 \\\Leftrightarrow & x = \frac{91}{1368} & & \\ & V = \left\{ \frac{91}{1368} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{4})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -9x+\frac{9}{4}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{+27} & = & \color{red}{60x} +32 \\\Leftrightarrow & -108x \color{red}{+27} \color{blue}{-27} \color{blue}{-60x} & = & \color{red}{60x} +32 \color{blue}{-60x} \color{blue}{-27} \\\Leftrightarrow & -108x-60x& = & 32-27 \\\Leftrightarrow & \color{red}{-168} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-168} & & \\\Leftrightarrow & x = \frac{-5}{168} & & \\ & V = \left\{ \frac{-5}{168} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{11})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 24x+\frac{30}{11}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+120} & = & \color{red}{220x} +77 \\\Leftrightarrow & 1056x \color{red}{+120} \color{blue}{-120} \color{blue}{-220x} & = & \color{red}{220x} +77 \color{blue}{-220x} \color{blue}{-120} \\\Leftrightarrow & 1056x-220x& = & 77-120 \\\Leftrightarrow & \color{red}{836} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{836} & & \\ & V = \left\{ \frac{-43}{836} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{360}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 360x \color{red}{+144} & = & \color{red}{300x} +25 \\\Leftrightarrow & 360x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +25 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & 360x-300x& = & 25-144 \\\Leftrightarrow & \color{red}{60} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{60} & & \\ & V = \left\{ \frac{-119}{60} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-90} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 594x \color{red}{-90} \color{blue}{+90} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+90} \\\Leftrightarrow & 594x+165x& = & 44+90 \\\Leftrightarrow & \color{red}{759} x& = & 134 \\\Leftrightarrow & x = \frac{134}{759} & & \\ & V = \left\{ \frac{134}{759} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-66} & = & \color{red}{385x} +42 \\\Leftrightarrow & 462x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & 462x-385x& = & 42+66 \\\Leftrightarrow & \color{red}{77} x& = & 108 \\\Leftrightarrow & x = \frac{108}{77} & & \\ & V = \left\{ \frac{108}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{9})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 21x+\frac{28}{9}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+140} & = & \color{red}{90x} +36 \\\Leftrightarrow & 945x \color{red}{+140} \color{blue}{-140} \color{blue}{-90x} & = & \color{red}{90x} +36 \color{blue}{-90x} \color{blue}{-140} \\\Leftrightarrow & 945x-90x& = & 36-140 \\\Leftrightarrow & \color{red}{855} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{855} & & \\ & V = \left\{ \frac{-104}{855} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{3})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-88} & = & \color{red}{99x} +15 \\\Leftrightarrow & -264x \color{red}{-88} \color{blue}{+88} \color{blue}{-99x} & = & \color{red}{99x} +15 \color{blue}{-99x} \color{blue}{+88} \\\Leftrightarrow & -264x-99x& = & 15+88 \\\Leftrightarrow & \color{red}{-363} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-363} & & \\\Leftrightarrow & x = \frac{-103}{363} & & \\ & V = \left\{ \frac{-103}{363} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{9})& = & 4x+\frac{3}{7} \\\Leftrightarrow & 15x-\frac{25}{9}& = & 4x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-175} & = & \color{red}{252x} +27 \\\Leftrightarrow & 945x \color{red}{-175} \color{blue}{+175} \color{blue}{-252x} & = & \color{red}{252x} +27 \color{blue}{-252x} \color{blue}{+175} \\\Leftrightarrow & 945x-252x& = & 27+175 \\\Leftrightarrow & \color{red}{693} x& = & 202 \\\Leftrightarrow & x = \frac{202}{693} & & \\ & V = \left\{ \frac{202}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & 240x+70x& = & 45+24 \\\Leftrightarrow & \color{red}{310} x& = & 69 \\\Leftrightarrow & x = \frac{69}{310} & & \\ & V = \left\{ \frac{69}{310} \right\} & \\\end{align}\)