Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{10})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -9x+\frac{9}{10}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+9} & = & \color{red}{70x} +14 \\\Leftrightarrow & -90x \color{red}{+9} \color{blue}{-9} \color{blue}{-70x} & = & \color{red}{70x} +14 \color{blue}{-70x} \color{blue}{-9} \\\Leftrightarrow & -90x-70x& = & 14-9 \\\Leftrightarrow & \color{red}{-160} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-160} & & \\\Leftrightarrow & x = \frac{-1}{32} & & \\ & V = \left\{ \frac{-1}{32} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{72}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+72} & = & \color{red}{105x} +28 \\\Leftrightarrow & 504x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 504x-105x& = & 28-72 \\\Leftrightarrow & \color{red}{399} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{399} & & \\ & V = \left\{ \frac{-44}{399} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-40} & = & \color{red}{225x} +18 \\\Leftrightarrow & 720x \color{red}{-40} \color{blue}{+40} \color{blue}{-225x} & = & \color{red}{225x} +18 \color{blue}{-225x} \color{blue}{+40} \\\Leftrightarrow & 720x-225x& = & 18+40 \\\Leftrightarrow & \color{red}{495} x& = & 58 \\\Leftrightarrow & x = \frac{58}{495} & & \\ & V = \left\{ \frac{58}{495} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -126x+147x& = & 28-30 \\\Leftrightarrow & \color{red}{21} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-16} & = & \color{red}{-42x} +7 \\\Leftrightarrow & -60x \color{red}{-16} \color{blue}{+16} \color{blue}{+42x} & = & \color{red}{-42x} +7 \color{blue}{+42x} \color{blue}{+16} \\\Leftrightarrow & -60x+42x& = & 7+16 \\\Leftrightarrow & \color{red}{-18} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-18} & & \\\Leftrightarrow & x = \frac{-23}{18} & & \\ & V = \left\{ \frac{-23}{18} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{-99x} +18 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & 924x+99x& = & 18-154 \\\Leftrightarrow & \color{red}{1023} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{1023} & & \\ & V = \left\{ \frac{-136}{1023} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -2x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-14} & = & \color{red}{-6x} +4 \\\Leftrightarrow & -84x \color{red}{-14} \color{blue}{+14} \color{blue}{+6x} & = & \color{red}{-6x} +4 \color{blue}{+6x} \color{blue}{+14} \\\Leftrightarrow & -84x+6x& = & 4+14 \\\Leftrightarrow & \color{red}{-78} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-78} & & \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 20x-\frac{16}{3}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-112} & = & \color{red}{147x} +6 \\\Leftrightarrow & 420x \color{red}{-112} \color{blue}{+112} \color{blue}{-147x} & = & \color{red}{147x} +6 \color{blue}{-147x} \color{blue}{+112} \\\Leftrightarrow & 420x-147x& = & 6+112 \\\Leftrightarrow & \color{red}{273} x& = & 118 \\\Leftrightarrow & x = \frac{118}{273} & & \\ & V = \left\{ \frac{118}{273} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{2})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -25x+\frac{15}{2}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+135} & = & \color{red}{162x} +16 \\\Leftrightarrow & -450x \color{red}{+135} \color{blue}{-135} \color{blue}{-162x} & = & \color{red}{162x} +16 \color{blue}{-162x} \color{blue}{-135} \\\Leftrightarrow & -450x-162x& = & 16-135 \\\Leftrightarrow & \color{red}{-612} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-612} & & \\\Leftrightarrow & x = \frac{7}{36} & & \\ & V = \left\{ \frac{7}{36} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+100} & = & \color{red}{135x} +18 \\\Leftrightarrow & -120x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & -120x-135x& = & 18-100 \\\Leftrightarrow & \color{red}{-255} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-255} & & \\\Leftrightarrow & x = \frac{82}{255} & & \\ & V = \left\{ \frac{82}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{-245x} +15 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & -210x+245x& = & 15-84 \\\Leftrightarrow & \color{red}{35} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{35} & & \\ & V = \left\{ \frac{-69}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 4x-\frac{6}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-42} & = & \color{red}{385x} +88 \\\Leftrightarrow & 308x \color{red}{-42} \color{blue}{+42} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+42} \\\Leftrightarrow & 308x-385x& = & 88+42 \\\Leftrightarrow & \color{red}{-77} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-77} & & \\\Leftrightarrow & x = \frac{-130}{77} & & \\ & V = \left\{ \frac{-130}{77} \right\} & \\\end{align}\)