Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{15}{8}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+105} & = & \color{red}{-168x} +64 \\\Leftrightarrow & 560x \color{red}{+105} \color{blue}{-105} \color{blue}{+168x} & = & \color{red}{-168x} +64 \color{blue}{+168x} \color{blue}{-105} \\\Leftrightarrow & 560x+168x& = & 64-105 \\\Leftrightarrow & \color{red}{728} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{728} & & \\ & V = \left\{ \frac{-41}{728} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-189x} +28 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+60} \\\Leftrightarrow & 420x+189x& = & 28+60 \\\Leftrightarrow & \color{red}{609} x& = & 88 \\\Leftrightarrow & x = \frac{88}{609} & & \\ & V = \left\{ \frac{88}{609} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +3 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 3-6 \\\Leftrightarrow & \color{red}{-119} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-119} & & \\\Leftrightarrow & x = \frac{3}{119} & & \\ & V = \left\{ \frac{3}{119} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-18} \\\Leftrightarrow & -120x+50x& = & 15-18 \\\Leftrightarrow & \color{red}{-70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-70} & & \\\Leftrightarrow & x = \frac{3}{70} & & \\ & V = \left\{ \frac{3}{70} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 3x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{+36} & = & \color{red}{126x} +35 \\\Leftrightarrow & 420x \color{red}{+36} \color{blue}{-36} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-36} \\\Leftrightarrow & 420x-126x& = & 35-36 \\\Leftrightarrow & \color{red}{294} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{294} & & \\ & V = \left\{ \frac{-1}{294} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+100} & = & \color{red}{105x} +18 \\\Leftrightarrow & -240x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & -240x-105x& = & 18-100 \\\Leftrightarrow & \color{red}{-345} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-345} & & \\\Leftrightarrow & x = \frac{82}{345} & & \\ & V = \left\{ \frac{82}{345} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{7})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+264} & = & \color{red}{-539x} +49 \\\Leftrightarrow & -2310x \color{red}{+264} \color{blue}{-264} \color{blue}{+539x} & = & \color{red}{-539x} +49 \color{blue}{+539x} \color{blue}{-264} \\\Leftrightarrow & -2310x+539x& = & 49-264 \\\Leftrightarrow & \color{red}{-1771} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{-1771} & & \\\Leftrightarrow & x = \frac{215}{1771} & & \\ & V = \left\{ \frac{215}{1771} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & 4x+\frac{3}{11} \\\Leftrightarrow & -15x+\frac{6}{11}& = & 4x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+6} & = & \color{red}{44x} +3 \\\Leftrightarrow & -165x \color{red}{+6} \color{blue}{-6} \color{blue}{-44x} & = & \color{red}{44x} +3 \color{blue}{-44x} \color{blue}{-6} \\\Leftrightarrow & -165x-44x& = & 3-6 \\\Leftrightarrow & \color{red}{-209} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-209} & & \\\Leftrightarrow & x = \frac{3}{209} & & \\ & V = \left\{ \frac{3}{209} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{2})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{25}{2}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x+ \frac{25}{ \color{blue}{2} })& = & (\frac{8}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{+25} & = & \color{red}{8x} +7 \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-8x} & = & \color{red}{8x} +7 \color{blue}{-8x} \color{blue}{-25} \\\Leftrightarrow & -30x-8x& = & 7-25 \\\Leftrightarrow & \color{red}{-38} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-38} & & \\\Leftrightarrow & x = \frac{9}{19} & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-72} & = & \color{red}{105x} +40 \\\Leftrightarrow & -450x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & -450x-105x& = & 40+72 \\\Leftrightarrow & \color{red}{-555} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-555} & & \\\Leftrightarrow & x = \frac{-112}{555} & & \\ & V = \left\{ \frac{-112}{555} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{7})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{15}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+165} & = & \color{red}{385x} +28 \\\Leftrightarrow & 462x \color{red}{+165} \color{blue}{-165} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-165} \\\Leftrightarrow & 462x-385x& = & 28-165 \\\Leftrightarrow & \color{red}{77} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{77} & & \\ & V = \left\{ \frac{-137}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -6x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -6x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{-100} & = & \color{red}{-210x} +42 \\\Leftrightarrow & 875x \color{red}{-100} \color{blue}{+100} \color{blue}{+210x} & = & \color{red}{-210x} +42 \color{blue}{+210x} \color{blue}{+100} \\\Leftrightarrow & 875x+210x& = & 42+100 \\\Leftrightarrow & \color{red}{1085} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1085} & & \\ & V = \left\{ \frac{142}{1085} \right\} & \\\end{align}\)