Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{20}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+60} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -210x \color{red}{+60} \color{blue}{-60} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-60} \\\Leftrightarrow & -210x+147x& = & 56-60 \\\Leftrightarrow & \color{red}{-63} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-63} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+48} & = & \color{red}{-63x} +14 \\\Leftrightarrow & -168x \color{red}{+48} \color{blue}{-48} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-48} \\\Leftrightarrow & -168x+63x& = & 14-48 \\\Leftrightarrow & \color{red}{-105} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-105} & & \\\Leftrightarrow & x = \frac{34}{105} & & \\ & V = \left\{ \frac{34}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 30-132 \\\Leftrightarrow & \color{red}{-385} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-385} & & \\\Leftrightarrow & x = \frac{102}{385} & & \\ & V = \left\{ \frac{102}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 6x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-385} & = & \color{red}{594x} +54 \\\Leftrightarrow & -3465x \color{red}{-385} \color{blue}{+385} \color{blue}{-594x} & = & \color{red}{594x} +54 \color{blue}{-594x} \color{blue}{+385} \\\Leftrightarrow & -3465x-594x& = & 54+385 \\\Leftrightarrow & \color{red}{-4059} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-4059} & & \\\Leftrightarrow & x = \frac{-439}{4059} & & \\ & V = \left\{ \frac{-439}{4059} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 16x-\frac{20}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{-20} & = & \color{red}{27x} +8 \\\Leftrightarrow & 48x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & 48x-27x& = & 8+20 \\\Leftrightarrow & \color{red}{21} x& = & 28 \\\Leftrightarrow & x = \frac{28}{21} & & \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+48} & = & \color{red}{-392x} +63 \\\Leftrightarrow & -560x \color{red}{+48} \color{blue}{-48} \color{blue}{+392x} & = & \color{red}{-392x} +63 \color{blue}{+392x} \color{blue}{-48} \\\Leftrightarrow & -560x+392x& = & 63-48 \\\Leftrightarrow & \color{red}{-168} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-168} & & \\\Leftrightarrow & x = \frac{-5}{56} & & \\ & V = \left\{ \frac{-5}{56} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{9}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +9 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +9 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 9-12 \\\Leftrightarrow & \color{red}{-85} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-85} & & \\\Leftrightarrow & x = \frac{3}{85} & & \\ & V = \left\{ \frac{3}{85} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{10}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-20} & = & \color{red}{-66x} +55 \\\Leftrightarrow & 440x \color{red}{-20} \color{blue}{+20} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{+20} \\\Leftrightarrow & 440x+66x& = & 55+20 \\\Leftrightarrow & \color{red}{506} x& = & 75 \\\Leftrightarrow & x = \frac{75}{506} & & \\ & V = \left\{ \frac{75}{506} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-147x} +49 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +49 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -210x+147x& = & 49-30 \\\Leftrightarrow & \color{red}{-63} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-63} & & \\\Leftrightarrow & x = \frac{-19}{63} & & \\ & V = \left\{ \frac{-19}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-8} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -144x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -144x+63x& = & 12+8 \\\Leftrightarrow & \color{red}{-81} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-81} & & \\\Leftrightarrow & x = \frac{-20}{81} & & \\ & V = \left\{ \frac{-20}{81} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+150} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & 420x+175x& = & 42-150 \\\Leftrightarrow & \color{red}{595} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{595} & & \\ & V = \left\{ \frac{-108}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-42} & = & \color{red}{245x} +45 \\\Leftrightarrow & -210x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & -210x-245x& = & 45+42 \\\Leftrightarrow & \color{red}{-455} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-455} & & \\\Leftrightarrow & x = \frac{-87}{455} & & \\ & V = \left\{ \frac{-87}{455} \right\} & \\\end{align}\)