Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 30x+\frac{18}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x+ \frac{18}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{+18} & = & \color{red}{49x} +2 \\\Leftrightarrow & 210x \color{red}{+18} \color{blue}{-18} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{-18} \\\Leftrightarrow & 210x-49x& = & 2-18 \\\Leftrightarrow & \color{red}{161} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{161} & & \\ & V = \left\{ \frac{-16}{161} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{3})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 4x-\frac{4}{3}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{44}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-44} & = & \color{red}{-165x} +15 \\\Leftrightarrow & 132x \color{red}{-44} \color{blue}{+44} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{+44} \\\Leftrightarrow & 132x+165x& = & 15+44 \\\Leftrightarrow & \color{red}{297} x& = & 59 \\\Leftrightarrow & x = \frac{59}{297} & & \\ & V = \left\{ \frac{59}{297} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{9})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -25x-\frac{20}{9}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1125}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1125x \color{red}{-100} & = & \color{red}{-180x} +81 \\\Leftrightarrow & -1125x \color{red}{-100} \color{blue}{+100} \color{blue}{+180x} & = & \color{red}{-180x} +81 \color{blue}{+180x} \color{blue}{+100} \\\Leftrightarrow & -1125x+180x& = & 81+100 \\\Leftrightarrow & \color{red}{-945} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-945} & & \\\Leftrightarrow & x = \frac{-181}{945} & & \\ & V = \left\{ \frac{-181}{945} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 90x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{115} & & \\ & V = \left\{ \frac{18}{115} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{2})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{21}{2}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+63} & = & \color{red}{-18x} +20 \\\Leftrightarrow & -84x \color{red}{+63} \color{blue}{-63} \color{blue}{+18x} & = & \color{red}{-18x} +20 \color{blue}{+18x} \color{blue}{-63} \\\Leftrightarrow & -84x+18x& = & 20-63 \\\Leftrightarrow & \color{red}{-66} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-66} & & \\\Leftrightarrow & x = \frac{43}{66} & & \\ & V = \left\{ \frac{43}{66} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+168} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 1386x \color{red}{+168} \color{blue}{-168} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-168} \\\Leftrightarrow & 1386x+385x& = & 110-168 \\\Leftrightarrow & \color{red}{1771} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1771} & & \\ & V = \left\{ \frac{-58}{1771} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -24x-\frac{24}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{-72} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -504x \color{red}{-72} \color{blue}{+72} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{+72} \\\Leftrightarrow & -504x+105x& = & 28+72 \\\Leftrightarrow & \color{red}{-399} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-399} & & \\\Leftrightarrow & x = \frac{-100}{399} & & \\ & V = \left\{ \frac{-100}{399} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{15}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-165} & = & \color{red}{385x} +35 \\\Leftrightarrow & -924x \color{red}{-165} \color{blue}{+165} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{+165} \\\Leftrightarrow & -924x-385x& = & 35+165 \\\Leftrightarrow & \color{red}{-1309} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1309} & & \\\Leftrightarrow & x = \frac{-200}{1309} & & \\ & V = \left\{ \frac{-200}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+80} & = & \color{red}{105x} +42 \\\Leftrightarrow & -700x \color{red}{+80} \color{blue}{-80} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{-80} \\\Leftrightarrow & -700x-105x& = & 42-80 \\\Leftrightarrow & \color{red}{-805} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-805} & & \\\Leftrightarrow & x = \frac{38}{805} & & \\ & V = \left\{ \frac{38}{805} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x- \frac{54}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{-54} & = & \color{red}{120x} +25 \\\Leftrightarrow & -450x \color{red}{-54} \color{blue}{+54} \color{blue}{-120x} & = & \color{red}{120x} +25 \color{blue}{-120x} \color{blue}{+54} \\\Leftrightarrow & -450x-120x& = & 25+54 \\\Leftrightarrow & \color{red}{-570} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-570} & & \\\Leftrightarrow & x = \frac{-79}{570} & & \\ & V = \left\{ \frac{-79}{570} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{32x} +3 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +3 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & -60x-32x& = & 3+15 \\\Leftrightarrow & \color{red}{-92} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-92} & & \\\Leftrightarrow & x = \frac{-9}{46} & & \\ & V = \left\{ \frac{-9}{46} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -120x+135x& = & 10+36 \\\Leftrightarrow & \color{red}{15} x& = & 46 \\\Leftrightarrow & x = \frac{46}{15} & & \\ & V = \left\{ \frac{46}{15} \right\} & \\\end{align}\)