Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{9})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 16x-\frac{16}{9}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{80}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-80} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 720x \color{red}{-80} \color{blue}{+80} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+80} \\\Leftrightarrow & 720x+315x& = & 18+80 \\\Leftrightarrow & \color{red}{1035} x& = & 98 \\\Leftrightarrow & x = \frac{98}{1035} & & \\ & V = \left\{ \frac{98}{1035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{12}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-60} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -330x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & -330x+385x& = & 22+60 \\\Leftrightarrow & \color{red}{55} x& = & 82 \\\Leftrightarrow & x = \frac{82}{55} & & \\ & V = \left\{ \frac{82}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{4})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{48}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 48x \color{red}{-15} & = & \color{red}{20x} +5 \\\Leftrightarrow & 48x \color{red}{-15} \color{blue}{+15} \color{blue}{-20x} & = & \color{red}{20x} +5 \color{blue}{-20x} \color{blue}{+15} \\\Leftrightarrow & 48x-20x& = & 5+15 \\\Leftrightarrow & \color{red}{28} x& = & 20 \\\Leftrightarrow & x = \frac{20}{28} & & \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{539x} +21 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1232x-539x& = & 21+176 \\\Leftrightarrow & \color{red}{-1771} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1771} & & \\\Leftrightarrow & x = \frac{-197}{1771} & & \\ & V = \left\{ \frac{-197}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 180x+105x& = & 10-36 \\\Leftrightarrow & \color{red}{285} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{285} & & \\ & V = \left\{ \frac{-26}{285} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & 4x+\frac{9}{7} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 4x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+140} & = & \color{red}{84x} +27 \\\Leftrightarrow & 315x \color{red}{+140} \color{blue}{-140} \color{blue}{-84x} & = & \color{red}{84x} +27 \color{blue}{-84x} \color{blue}{-140} \\\Leftrightarrow & 315x-84x& = & 27-140 \\\Leftrightarrow & \color{red}{231} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{231} & & \\ & V = \left\{ \frac{-113}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{6})& = & -8x+\frac{9}{2} \\\Leftrightarrow & -21x+\frac{35}{6}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{-48x} +27 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{+48x} & = & \color{red}{-48x} +27 \color{blue}{+48x} \color{blue}{-35} \\\Leftrightarrow & -126x+48x& = & 27-35 \\\Leftrightarrow & \color{red}{-78} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-78} & & \\\Leftrightarrow & x = \frac{4}{39} & & \\ & V = \left\{ \frac{4}{39} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{+165} & = & \color{red}{-396x} +16 \\\Leftrightarrow & 440x \color{red}{+165} \color{blue}{-165} \color{blue}{+396x} & = & \color{red}{-396x} +16 \color{blue}{+396x} \color{blue}{-165} \\\Leftrightarrow & 440x+396x& = & 16-165 \\\Leftrightarrow & \color{red}{836} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{836} & & \\ & V = \left\{ \frac{-149}{836} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+330} & = & \color{red}{-385x} +28 \\\Leftrightarrow & 1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & 1848x+385x& = & 28-330 \\\Leftrightarrow & \color{red}{2233} x& = & -302 \\\Leftrightarrow & x = \frac{-302}{2233} & & \\ & V = \left\{ \frac{-302}{2233} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-288}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -288x \color{red}{+64} & = & \color{red}{360x} +63 \\\Leftrightarrow & -288x \color{red}{+64} \color{blue}{-64} \color{blue}{-360x} & = & \color{red}{360x} +63 \color{blue}{-360x} \color{blue}{-64} \\\Leftrightarrow & -288x-360x& = & 63-64 \\\Leftrightarrow & \color{red}{-648} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-648} & & \\\Leftrightarrow & x = \frac{1}{648} & & \\ & V = \left\{ \frac{1}{648} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{28}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+28} & = & \color{red}{27x} +4 \\\Leftrightarrow & 42x \color{red}{+28} \color{blue}{-28} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{-28} \\\Leftrightarrow & 42x-27x& = & 4-28 \\\Leftrightarrow & \color{red}{15} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{15} & & \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-90} & = & \color{red}{-567x} +56 \\\Leftrightarrow & -1260x \color{red}{-90} \color{blue}{+90} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{+90} \\\Leftrightarrow & -1260x+567x& = & 56+90 \\\Leftrightarrow & \color{red}{-693} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-693} & & \\\Leftrightarrow & x = \frac{-146}{693} & & \\ & V = \left\{ \frac{-146}{693} \right\} & \\\end{align}\)