Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+150} & = & \color{red}{175x} +14 \\\Leftrightarrow & 630x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +14 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & 630x-175x& = & 14-150 \\\Leftrightarrow & \color{red}{455} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{455} & & \\ & V = \left\{ \frac{-136}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+30} & = & \color{red}{56x} +7 \\\Leftrightarrow & -160x \color{red}{+30} \color{blue}{-30} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{-30} \\\Leftrightarrow & -160x-56x& = & 7-30 \\\Leftrightarrow & \color{red}{-216} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-216} & & \\\Leftrightarrow & x = \frac{23}{216} & & \\ & V = \left\{ \frac{23}{216} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{27x} +8 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & 180x-27x& = & 8-8 \\\Leftrightarrow & \color{red}{153} x& = & 0 \\\Leftrightarrow & x = \frac{0}{153} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{20}{7}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+180} & = & \color{red}{567x} +28 \\\Leftrightarrow & 630x \color{red}{+180} \color{blue}{-180} \color{blue}{-567x} & = & \color{red}{567x} +28 \color{blue}{-567x} \color{blue}{-180} \\\Leftrightarrow & 630x-567x& = & 28-180 \\\Leftrightarrow & \color{red}{63} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{63} & & \\ & V = \left\{ \frac{-152}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{3})& = & -9x+\frac{3}{5} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-135x} +9 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+135x} & = & \color{red}{-135x} +9 \color{blue}{+135x} \color{blue}{-140} \\\Leftrightarrow & 420x+135x& = & 9-140 \\\Leftrightarrow & \color{red}{555} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{555} & & \\ & V = \left\{ \frac{-131}{555} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+60} & = & \color{red}{-63x} +70 \\\Leftrightarrow & -168x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +70 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & -168x+63x& = & 70-60 \\\Leftrightarrow & \color{red}{-105} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-105} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 150x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{115} & & \\ & V = \left\{ \frac{18}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-66} & = & \color{red}{385x} +15 \\\Leftrightarrow & -330x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -330x-385x& = & 15+66 \\\Leftrightarrow & \color{red}{-715} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-715} & & \\\Leftrightarrow & x = \frac{-81}{715} & & \\ & V = \left\{ \frac{-81}{715} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{-360x} +16 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+360x} & = & \color{red}{-360x} +16 \color{blue}{+360x} \color{blue}{-105} \\\Leftrightarrow & -1400x+360x& = & 16-105 \\\Leftrightarrow & \color{red}{-1040} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-1040} & & \\\Leftrightarrow & x = \frac{89}{1040} & & \\ & V = \left\{ \frac{89}{1040} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-40} & = & \color{red}{196x} +49 \\\Leftrightarrow & 224x \color{red}{-40} \color{blue}{+40} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{+40} \\\Leftrightarrow & 224x-196x& = & 49+40 \\\Leftrightarrow & \color{red}{28} x& = & 89 \\\Leftrightarrow & x = \frac{89}{28} & & \\ & V = \left\{ \frac{89}{28} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & -63x+35x& = & 10+6 \\\Leftrightarrow & \color{red}{-28} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-28} & & \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & -9x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1400}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1400x \color{red}{+100} & = & \color{red}{-630x} +63 \\\Leftrightarrow & 1400x \color{red}{+100} \color{blue}{-100} \color{blue}{+630x} & = & \color{red}{-630x} +63 \color{blue}{+630x} \color{blue}{-100} \\\Leftrightarrow & 1400x+630x& = & 63-100 \\\Leftrightarrow & \color{red}{2030} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{2030} & & \\ & V = \left\{ \frac{-37}{2030} \right\} & \\\end{align}\)