Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{4}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+4} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -30x \color{red}{+4} \color{blue}{-4} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-4} \\\Leftrightarrow & -30x+21x& = & 10-4 \\\Leftrightarrow & \color{red}{-9} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-9} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-168}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -168x \color{red}{+36} & = & \color{red}{-210x} +35 \\\Leftrightarrow & -168x \color{red}{+36} \color{blue}{-36} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-36} \\\Leftrightarrow & -168x+210x& = & 35-36 \\\Leftrightarrow & \color{red}{42} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{42} & & \\ & V = \left\{ \frac{-1}{42} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{11})& = & 2x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{15}{11}& = & 2x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{-60} & = & \color{red}{88x} +99 \\\Leftrightarrow & -1100x \color{red}{-60} \color{blue}{+60} \color{blue}{-88x} & = & \color{red}{88x} +99 \color{blue}{-88x} \color{blue}{+60} \\\Leftrightarrow & -1100x-88x& = & 99+60 \\\Leftrightarrow & \color{red}{-1188} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-1188} & & \\\Leftrightarrow & x = \frac{-53}{396} & & \\ & V = \left\{ \frac{-53}{396} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x+\frac{30}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+210} & = & \color{red}{539x} +110 \\\Leftrightarrow & 2310x \color{red}{+210} \color{blue}{-210} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-210} \\\Leftrightarrow & 2310x-539x& = & 110-210 \\\Leftrightarrow & \color{red}{1771} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{1771} & & \\ & V = \left\{ \frac{-100}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-36} \\\Leftrightarrow & -270x+315x& = & 50-36 \\\Leftrightarrow & \color{red}{45} x& = & 14 \\\Leftrightarrow & x = \frac{14}{45} & & \\ & V = \left\{ \frac{14}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 8x+\frac{16}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{112}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+112} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 280x \color{red}{+112} \color{blue}{-112} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{-112} \\\Leftrightarrow & 280x+175x& = & 40-112 \\\Leftrightarrow & \color{red}{455} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{455} & & \\ & V = \left\{ \frac{-72}{455} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & 6x+\frac{5}{2} \\\Leftrightarrow & 35x-\frac{21}{11}& = & 6x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{770}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{132}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 770x \color{red}{-42} & = & \color{red}{132x} +55 \\\Leftrightarrow & 770x \color{red}{-42} \color{blue}{+42} \color{blue}{-132x} & = & \color{red}{132x} +55 \color{blue}{-132x} \color{blue}{+42} \\\Leftrightarrow & 770x-132x& = & 55+42 \\\Leftrightarrow & \color{red}{638} x& = & 97 \\\Leftrightarrow & x = \frac{97}{638} & & \\ & V = \left\{ \frac{97}{638} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & 6x+\frac{5}{2} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 6x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{60}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+24} & = & \color{red}{60x} +25 \\\Leftrightarrow & -180x \color{red}{+24} \color{blue}{-24} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{-24} \\\Leftrightarrow & -180x-60x& = & 25-24 \\\Leftrightarrow & \color{red}{-240} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-240} & & \\\Leftrightarrow & x = \frac{-1}{240} & & \\ & V = \left\{ \frac{-1}{240} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+105} & = & \color{red}{196x} +40 \\\Leftrightarrow & -168x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +40 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & -168x-196x& = & 40-105 \\\Leftrightarrow & \color{red}{-364} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-364} & & \\\Leftrightarrow & x = \frac{5}{28} & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{-75} & = & \color{red}{360x} +36 \\\Leftrightarrow & 800x \color{red}{-75} \color{blue}{+75} \color{blue}{-360x} & = & \color{red}{360x} +36 \color{blue}{-360x} \color{blue}{+75} \\\Leftrightarrow & 800x-360x& = & 36+75 \\\Leftrightarrow & \color{red}{440} x& = & 111 \\\Leftrightarrow & x = \frac{111}{440} & & \\ & V = \left\{ \frac{111}{440} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 2x+\frac{5}{7} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 2x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{+10} & = & \color{red}{14x} +5 \\\Leftrightarrow & 175x \color{red}{+10} \color{blue}{-10} \color{blue}{-14x} & = & \color{red}{14x} +5 \color{blue}{-14x} \color{blue}{-10} \\\Leftrightarrow & 175x-14x& = & 5-10 \\\Leftrightarrow & \color{red}{161} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{161} & & \\ & V = \left\{ \frac{-5}{161} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-88} & = & \color{red}{-891x} +45 \\\Leftrightarrow & 1584x \color{red}{-88} \color{blue}{+88} \color{blue}{+891x} & = & \color{red}{-891x} +45 \color{blue}{+891x} \color{blue}{+88} \\\Leftrightarrow & 1584x+891x& = & 45+88 \\\Leftrightarrow & \color{red}{2475} x& = & 133 \\\Leftrightarrow & x = \frac{133}{2475} & & \\ & V = \left\{ \frac{133}{2475} \right\} & \\\end{align}\)