Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{-220} & = & \color{red}{66x} +18 \\\Leftrightarrow & 825x \color{red}{-220} \color{blue}{+220} \color{blue}{-66x} & = & \color{red}{66x} +18 \color{blue}{-66x} \color{blue}{+220} \\\Leftrightarrow & 825x-66x& = & 18+220 \\\Leftrightarrow & \color{red}{759} x& = & 238 \\\Leftrightarrow & x = \frac{238}{759} & & \\ & V = \left\{ \frac{238}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & 3x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-50} & = & \color{red}{165x} +88 \\\Leftrightarrow & -1100x \color{red}{-50} \color{blue}{+50} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+50} \\\Leftrightarrow & -1100x-165x& = & 88+50 \\\Leftrightarrow & \color{red}{-1265} x& = & 138 \\\Leftrightarrow & x = \frac{138}{-1265} & & \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 4x+\frac{10}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{220x} +50 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{-220x} & = & \color{red}{220x} +50 \color{blue}{-220x} \color{blue}{+132} \\\Leftrightarrow & 495x-220x& = & 50+132 \\\Leftrightarrow & \color{red}{275} x& = & 182 \\\Leftrightarrow & x = \frac{182}{275} & & \\ & V = \left\{ \frac{182}{275} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{539x} +42 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & -462x-539x& = & 42+66 \\\Leftrightarrow & \color{red}{-1001} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-1001} & & \\\Leftrightarrow & x = \frac{-108}{1001} & & \\ & V = \left\{ \frac{-108}{1001} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 2x+\frac{4}{11} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 2x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+330} & = & \color{red}{154x} +28 \\\Leftrightarrow & -1386x \color{red}{+330} \color{blue}{-330} \color{blue}{-154x} & = & \color{red}{154x} +28 \color{blue}{-154x} \color{blue}{-330} \\\Leftrightarrow & -1386x-154x& = & 28-330 \\\Leftrightarrow & \color{red}{-1540} x& = & -302 \\\Leftrightarrow & x = \frac{-302}{-1540} & & \\\Leftrightarrow & x = \frac{151}{770} & & \\ & V = \left\{ \frac{151}{770} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & 8x+\frac{7}{5} \\\Leftrightarrow & 35x+\frac{28}{11}& = & 8x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x+ \frac{140}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{+140} & = & \color{red}{440x} +77 \\\Leftrightarrow & 1925x \color{red}{+140} \color{blue}{-140} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{-140} \\\Leftrightarrow & 1925x-440x& = & 77-140 \\\Leftrightarrow & \color{red}{1485} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{1485} & & \\\Leftrightarrow & x = \frac{-7}{165} & & \\ & V = \left\{ \frac{-7}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 4x+\frac{4}{9} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{-270} & = & \color{red}{252x} +28 \\\Leftrightarrow & -1134x \color{red}{-270} \color{blue}{+270} \color{blue}{-252x} & = & \color{red}{252x} +28 \color{blue}{-252x} \color{blue}{+270} \\\Leftrightarrow & -1134x-252x& = & 28+270 \\\Leftrightarrow & \color{red}{-1386} x& = & 298 \\\Leftrightarrow & x = \frac{298}{-1386} & & \\\Leftrightarrow & x = \frac{-149}{693} & & \\ & V = \left\{ \frac{-149}{693} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{20}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+60} & = & \color{red}{-99x} +88 \\\Leftrightarrow & 264x \color{red}{+60} \color{blue}{-60} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{-60} \\\Leftrightarrow & 264x+99x& = & 88-60 \\\Leftrightarrow & \color{red}{363} x& = & 28 \\\Leftrightarrow & x = \frac{28}{363} & & \\ & V = \left\{ \frac{28}{363} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{-75x} +25 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +25 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 240x+75x& = & 25-36 \\\Leftrightarrow & \color{red}{315} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{315} & & \\ & V = \left\{ \frac{-11}{315} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{9})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{10}{9}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-70} & = & \color{red}{441x} +18 \\\Leftrightarrow & 378x \color{red}{-70} \color{blue}{+70} \color{blue}{-441x} & = & \color{red}{441x} +18 \color{blue}{-441x} \color{blue}{+70} \\\Leftrightarrow & 378x-441x& = & 18+70 \\\Leftrightarrow & \color{red}{-63} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-63} & & \\\Leftrightarrow & x = \frac{-88}{63} & & \\ & V = \left\{ \frac{-88}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-330} & = & \color{red}{385x} +42 \\\Leftrightarrow & 1386x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1386x-385x& = & 42+330 \\\Leftrightarrow & \color{red}{1001} x& = & 372 \\\Leftrightarrow & x = \frac{372}{1001} & & \\ & V = \left\{ \frac{372}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x+\frac{15}{2}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{10}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{+45} & = & \color{red}{-30x} +10 \\\Leftrightarrow & -72x \color{red}{+45} \color{blue}{-45} \color{blue}{+30x} & = & \color{red}{-30x} +10 \color{blue}{+30x} \color{blue}{-45} \\\Leftrightarrow & -72x+30x& = & 10-45 \\\Leftrightarrow & \color{red}{-42} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-42} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)