Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{9})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -12x-\frac{20}{9}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-100} & = & \color{red}{-225x} +81 \\\Leftrightarrow & -540x \color{red}{-100} \color{blue}{+100} \color{blue}{+225x} & = & \color{red}{-225x} +81 \color{blue}{+225x} \color{blue}{+100} \\\Leftrightarrow & -540x+225x& = & 81+100 \\\Leftrightarrow & \color{red}{-315} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-315} & & \\\Leftrightarrow & x = \frac{-181}{315} & & \\ & V = \left\{ \frac{-181}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-48} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{-48} \color{blue}{+48} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+48} \\\Leftrightarrow & 252x-105x& = & 14+48 \\\Leftrightarrow & \color{red}{147} x& = & 62 \\\Leftrightarrow & x = \frac{62}{147} & & \\ & V = \left\{ \frac{62}{147} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 60x-25x& = & 6+24 \\\Leftrightarrow & \color{red}{35} x& = & 30 \\\Leftrightarrow & x = \frac{30}{35} & & \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{15}{8}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+15} & = & \color{red}{56x} +7 \\\Leftrightarrow & -160x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & -160x-56x& = & 7-15 \\\Leftrightarrow & \color{red}{-216} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-216} & & \\\Leftrightarrow & x = \frac{1}{27} & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +70 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 70+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 340 \\\Leftrightarrow & x = \frac{340}{-1197} & & \\\Leftrightarrow & x = \frac{-340}{1197} & & \\ & V = \left\{ \frac{-340}{1197} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{8}{3}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-80} & = & \color{red}{150x} +9 \\\Leftrightarrow & -360x \color{red}{-80} \color{blue}{+80} \color{blue}{-150x} & = & \color{red}{150x} +9 \color{blue}{-150x} \color{blue}{+80} \\\Leftrightarrow & -360x-150x& = & 9+80 \\\Leftrightarrow & \color{red}{-510} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-510} & & \\\Leftrightarrow & x = \frac{-89}{510} & & \\ & V = \left\{ \frac{-89}{510} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 21x+\frac{21}{11}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 231x \color{red}{+21} & = & \color{red}{-22x} +6 \\\Leftrightarrow & 231x \color{red}{+21} \color{blue}{-21} \color{blue}{+22x} & = & \color{red}{-22x} +6 \color{blue}{+22x} \color{blue}{-21} \\\Leftrightarrow & 231x+22x& = & 6-21 \\\Leftrightarrow & \color{red}{253} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{253} & & \\ & V = \left\{ \frac{-15}{253} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+210} & = & \color{red}{385x} +33 \\\Leftrightarrow & 1386x \color{red}{+210} \color{blue}{-210} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{-210} \\\Leftrightarrow & 1386x-385x& = & 33-210 \\\Leftrightarrow & \color{red}{1001} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{1001} & & \\ & V = \left\{ \frac{-177}{1001} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{3})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{-210x} +9 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{+210x} & = & \color{red}{-210x} +9 \color{blue}{+210x} \color{blue}{+80} \\\Leftrightarrow & 240x+210x& = & 9+80 \\\Leftrightarrow & \color{red}{450} x& = & 89 \\\Leftrightarrow & x = \frac{89}{450} & & \\ & V = \left\{ \frac{89}{450} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{756}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 756x \color{red}{-180} & = & \color{red}{210x} +49 \\\Leftrightarrow & 756x \color{red}{-180} \color{blue}{+180} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{+180} \\\Leftrightarrow & 756x-210x& = & 49+180 \\\Leftrightarrow & \color{red}{546} x& = & 229 \\\Leftrightarrow & x = \frac{229}{546} & & \\ & V = \left\{ \frac{229}{546} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{4}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{4}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-4} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 88x \color{red}{-4} \color{blue}{+4} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+4} \\\Leftrightarrow & 88x+99x& = & 6+4 \\\Leftrightarrow & \color{red}{187} x& = & 10 \\\Leftrightarrow & x = \frac{10}{187} & & \\ & V = \left\{ \frac{10}{187} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{8})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{15}{8}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1760}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1760x \color{red}{-165} & = & \color{red}{616x} +16 \\\Leftrightarrow & -1760x \color{red}{-165} \color{blue}{+165} \color{blue}{-616x} & = & \color{red}{616x} +16 \color{blue}{-616x} \color{blue}{+165} \\\Leftrightarrow & -1760x-616x& = & 16+165 \\\Leftrightarrow & \color{red}{-2376} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-2376} & & \\\Leftrightarrow & x = \frac{-181}{2376} & & \\ & V = \left\{ \frac{-181}{2376} \right\} & \\\end{align}\)