Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+4} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -30x \color{red}{+4} \color{blue}{-4} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-4} \\\Leftrightarrow & -30x+35x& = & 4-4 \\\Leftrightarrow & \color{red}{5} x& = & 0 \\\Leftrightarrow & x = \frac{0}{5} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-8} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & -12x+27x& = & 4+8 \\\Leftrightarrow & \color{red}{15} x& = & 12 \\\Leftrightarrow & x = \frac{12}{15} & & \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+220} & = & \color{red}{-539x} +28 \\\Leftrightarrow & 770x \color{red}{+220} \color{blue}{-220} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-220} \\\Leftrightarrow & 770x+539x& = & 28-220 \\\Leftrightarrow & \color{red}{1309} x& = & -192 \\\Leftrightarrow & x = \frac{-192}{1309} & & \\ & V = \left\{ \frac{-192}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-50} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 550x \color{red}{-50} \color{blue}{+50} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+50} \\\Leftrightarrow & 550x+495x& = & 22+50 \\\Leftrightarrow & \color{red}{1045} x& = & 72 \\\Leftrightarrow & x = \frac{72}{1045} & & \\ & V = \left\{ \frac{72}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{9})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -35x+\frac{28}{9}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+28} & = & \color{red}{-27x} +6 \\\Leftrightarrow & -315x \color{red}{+28} \color{blue}{-28} \color{blue}{+27x} & = & \color{red}{-27x} +6 \color{blue}{+27x} \color{blue}{-28} \\\Leftrightarrow & -315x+27x& = & 6-28 \\\Leftrightarrow & \color{red}{-288} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-288} & & \\\Leftrightarrow & x = \frac{11}{144} & & \\ & V = \left\{ \frac{11}{144} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+330} & = & \color{red}{385x} +49 \\\Leftrightarrow & -1848x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & -1848x-385x& = & 49-330 \\\Leftrightarrow & \color{red}{-2233} x& = & -281 \\\Leftrightarrow & x = \frac{-281}{-2233} & & \\\Leftrightarrow & x = \frac{281}{2233} & & \\ & V = \left\{ \frac{281}{2233} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+70} & = & \color{red}{539x} +88 \\\Leftrightarrow & -770x \color{red}{+70} \color{blue}{-70} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-70} \\\Leftrightarrow & -770x-539x& = & 88-70 \\\Leftrightarrow & \color{red}{-1309} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-1309} & & \\\Leftrightarrow & x = \frac{-18}{1309} & & \\ & V = \left\{ \frac{-18}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{11})& = & -3x+\frac{5}{4} \\\Leftrightarrow & 28x-\frac{14}{11}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x- \frac{56}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{-56} & = & \color{red}{-132x} +55 \\\Leftrightarrow & 1232x \color{red}{-56} \color{blue}{+56} \color{blue}{+132x} & = & \color{red}{-132x} +55 \color{blue}{+132x} \color{blue}{+56} \\\Leftrightarrow & 1232x+132x& = & 55+56 \\\Leftrightarrow & \color{red}{1364} x& = & 111 \\\Leftrightarrow & x = \frac{111}{1364} & & \\ & V = \left\{ \frac{111}{1364} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{6}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-66} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -220x \color{red}{-66} \color{blue}{+66} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+66} \\\Leftrightarrow & -220x+275x& = & 30+66 \\\Leftrightarrow & \color{red}{55} x& = & 96 \\\Leftrightarrow & x = \frac{96}{55} & & \\ & V = \left\{ \frac{96}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{35x} +10 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 63x-35x& = & 10-6 \\\Leftrightarrow & \color{red}{28} x& = & 4 \\\Leftrightarrow & x = \frac{4}{28} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+30} & = & \color{red}{147x} +56 \\\Leftrightarrow & -420x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -420x-147x& = & 56-30 \\\Leftrightarrow & \color{red}{-567} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-567} & & \\\Leftrightarrow & x = \frac{-26}{567} & & \\ & V = \left\{ \frac{-26}{567} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-70} & = & \color{red}{-135x} +12 \\\Leftrightarrow & -420x \color{red}{-70} \color{blue}{+70} \color{blue}{+135x} & = & \color{red}{-135x} +12 \color{blue}{+135x} \color{blue}{+70} \\\Leftrightarrow & -420x+135x& = & 12+70 \\\Leftrightarrow & \color{red}{-285} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-285} & & \\\Leftrightarrow & x = \frac{-82}{285} & & \\ & V = \left\{ \frac{-82}{285} \right\} & \\\end{align}\)