Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & 420x+147x& = & 70-30 \\\Leftrightarrow & \color{red}{567} x& = & 40 \\\Leftrightarrow & x = \frac{40}{567} & & \\ & V = \left\{ \frac{40}{567} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{9})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{16}{9}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{112}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-112} & = & \color{red}{441x} +72 \\\Leftrightarrow & 504x \color{red}{-112} \color{blue}{+112} \color{blue}{-441x} & = & \color{red}{441x} +72 \color{blue}{-441x} \color{blue}{+112} \\\Leftrightarrow & 504x-441x& = & 72+112 \\\Leftrightarrow & \color{red}{63} x& = & 184 \\\Leftrightarrow & x = \frac{184}{63} & & \\ & V = \left\{ \frac{184}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+50} & = & \color{red}{315x} +63 \\\Leftrightarrow & -140x \color{red}{+50} \color{blue}{-50} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{-50} \\\Leftrightarrow & -140x-315x& = & 63-50 \\\Leftrightarrow & \color{red}{-455} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-455} & & \\\Leftrightarrow & x = \frac{-1}{35} & & \\ & V = \left\{ \frac{-1}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{5})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{8}{5}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+32} & = & \color{red}{-180x} +45 \\\Leftrightarrow & -400x \color{red}{+32} \color{blue}{-32} \color{blue}{+180x} & = & \color{red}{-180x} +45 \color{blue}{+180x} \color{blue}{-32} \\\Leftrightarrow & -400x+180x& = & 45-32 \\\Leftrightarrow & \color{red}{-220} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-220} & & \\\Leftrightarrow & x = \frac{-13}{220} & & \\ & V = \left\{ \frac{-13}{220} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{4})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{9}{4}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{27}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-27} & = & \color{red}{84x} +40 \\\Leftrightarrow & 144x \color{red}{-27} \color{blue}{+27} \color{blue}{-84x} & = & \color{red}{84x} +40 \color{blue}{-84x} \color{blue}{+27} \\\Leftrightarrow & 144x-84x& = & 40+27 \\\Leftrightarrow & \color{red}{60} x& = & 67 \\\Leftrightarrow & x = \frac{67}{60} & & \\ & V = \left\{ \frac{67}{60} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 28-66 \\\Leftrightarrow & \color{red}{77} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{77} & & \\ & V = \left\{ \frac{-38}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{70x} +3 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 150x-70x& = & 3-24 \\\Leftrightarrow & \color{red}{80} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{80} & & \\ & V = \left\{ \frac{-21}{80} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & 4x+\frac{4}{9} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-180} & = & \color{red}{252x} +28 \\\Leftrightarrow & 945x \color{red}{-180} \color{blue}{+180} \color{blue}{-252x} & = & \color{red}{252x} +28 \color{blue}{-252x} \color{blue}{+180} \\\Leftrightarrow & 945x-252x& = & 28+180 \\\Leftrightarrow & \color{red}{693} x& = & 208 \\\Leftrightarrow & x = \frac{208}{693} & & \\ & V = \left\{ \frac{208}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{7})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{20}{7}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-60} & = & \color{red}{168x} +28 \\\Leftrightarrow & -315x \color{red}{-60} \color{blue}{+60} \color{blue}{-168x} & = & \color{red}{168x} +28 \color{blue}{-168x} \color{blue}{+60} \\\Leftrightarrow & -315x-168x& = & 28+60 \\\Leftrightarrow & \color{red}{-483} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-483} & & \\\Leftrightarrow & x = \frac{-88}{483} & & \\ & V = \left\{ \frac{-88}{483} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{-90} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -504x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & -504x+105x& = & 14+90 \\\Leftrightarrow & \color{red}{-399} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-399} & & \\\Leftrightarrow & x = \frac{-104}{399} & & \\ & V = \left\{ \frac{-104}{399} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & 6x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{28}{11}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{28}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+28} & = & \color{red}{66x} +6 \\\Leftrightarrow & 385x \color{red}{+28} \color{blue}{-28} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{-28} \\\Leftrightarrow & 385x-66x& = & 6-28 \\\Leftrightarrow & \color{red}{319} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{319} & & \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{9})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+88} & = & \color{red}{-693x} +18 \\\Leftrightarrow & -1980x \color{red}{+88} \color{blue}{-88} \color{blue}{+693x} & = & \color{red}{-693x} +18 \color{blue}{+693x} \color{blue}{-88} \\\Leftrightarrow & -1980x+693x& = & 18-88 \\\Leftrightarrow & \color{red}{-1287} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-1287} & & \\\Leftrightarrow & x = \frac{70}{1287} & & \\ & V = \left\{ \frac{70}{1287} \right\} & \\\end{align}\)