Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & -2x+\frac{5}{11} \\\Leftrightarrow & 9x+\frac{15}{11}& = & -2x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{+15} & = & \color{red}{-22x} +5 \\\Leftrightarrow & 99x \color{red}{+15} \color{blue}{-15} \color{blue}{+22x} & = & \color{red}{-22x} +5 \color{blue}{+22x} \color{blue}{-15} \\\Leftrightarrow & 99x+22x& = & 5-15 \\\Leftrightarrow & \color{red}{121} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{121} & & \\ & V = \left\{ \frac{-10}{121} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -24x+\frac{12}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+60} & = & \color{red}{-175x} +14 \\\Leftrightarrow & -840x \color{red}{+60} \color{blue}{-60} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{-60} \\\Leftrightarrow & -840x+175x& = & 14-60 \\\Leftrightarrow & \color{red}{-665} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-665} & & \\\Leftrightarrow & x = \frac{46}{665} & & \\ & V = \left\{ \frac{46}{665} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{15}{4}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{+45} & = & \color{red}{-108x} +32 \\\Leftrightarrow & -240x \color{red}{+45} \color{blue}{-45} \color{blue}{+108x} & = & \color{red}{-108x} +32 \color{blue}{+108x} \color{blue}{-45} \\\Leftrightarrow & -240x+108x& = & 32-45 \\\Leftrightarrow & \color{red}{-132} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-132} & & \\\Leftrightarrow & x = \frac{13}{132} & & \\ & V = \left\{ \frac{13}{132} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & -630x+147x& = & 28+90 \\\Leftrightarrow & \color{red}{-483} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-483} & & \\\Leftrightarrow & x = \frac{-118}{483} & & \\ & V = \left\{ \frac{-118}{483} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & -8x+\frac{5}{9} \\\Leftrightarrow & 35x+\frac{28}{11}& = & -8x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x+ \frac{252}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{+252} & = & \color{red}{-792x} +55 \\\Leftrightarrow & 3465x \color{red}{+252} \color{blue}{-252} \color{blue}{+792x} & = & \color{red}{-792x} +55 \color{blue}{+792x} \color{blue}{-252} \\\Leftrightarrow & 3465x+792x& = & 55-252 \\\Leftrightarrow & \color{red}{4257} x& = & -197 \\\Leftrightarrow & x = \frac{-197}{4257} & & \\ & V = \left\{ \frac{-197}{4257} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+48} & = & \color{red}{180x} +45 \\\Leftrightarrow & -400x \color{red}{+48} \color{blue}{-48} \color{blue}{-180x} & = & \color{red}{180x} +45 \color{blue}{-180x} \color{blue}{-48} \\\Leftrightarrow & -400x-180x& = & 45-48 \\\Leftrightarrow & \color{red}{-580} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-580} & & \\\Leftrightarrow & x = \frac{3}{580} & & \\ & V = \left\{ \frac{3}{580} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{55x} +8 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & 198x-55x& = & 8+18 \\\Leftrightarrow & \color{red}{143} x& = & 26 \\\Leftrightarrow & x = \frac{26}{143} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{9}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+18} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 210x \color{red}{+18} \color{blue}{-18} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-18} \\\Leftrightarrow & 210x+98x& = & 21-18 \\\Leftrightarrow & \color{red}{308} x& = & 3 \\\Leftrightarrow & x = \frac{3}{308} & & \\ & V = \left\{ \frac{3}{308} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{245x} +50 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 210x-245x& = & 50+84 \\\Leftrightarrow & \color{red}{-35} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-35} & & \\\Leftrightarrow & x = \frac{-134}{35} & & \\ & V = \left\{ \frac{-134}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+80} & = & \color{red}{392x} +49 \\\Leftrightarrow & 336x \color{red}{+80} \color{blue}{-80} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{-80} \\\Leftrightarrow & 336x-392x& = & 49-80 \\\Leftrightarrow & \color{red}{-56} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-56} & & \\\Leftrightarrow & x = \frac{31}{56} & & \\ & V = \left\{ \frac{31}{56} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-54} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -594x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -594x+165x& = & 88+54 \\\Leftrightarrow & \color{red}{-429} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-429} & & \\\Leftrightarrow & x = \frac{-142}{429} & & \\ & V = \left\{ \frac{-142}{429} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & -6x+\frac{8}{11} \\\Leftrightarrow & 35x-\frac{35}{9}& = & -6x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{-594}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-385} & = & \color{red}{-594x} +72 \\\Leftrightarrow & 3465x \color{red}{-385} \color{blue}{+385} \color{blue}{+594x} & = & \color{red}{-594x} +72 \color{blue}{+594x} \color{blue}{+385} \\\Leftrightarrow & 3465x+594x& = & 72+385 \\\Leftrightarrow & \color{red}{4059} x& = & 457 \\\Leftrightarrow & x = \frac{457}{4059} & & \\ & V = \left\{ \frac{457}{4059} \right\} & \\\end{align}\)