Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & -4x+\frac{2}{7} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -4x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+10} & = & \color{red}{-28x} +2 \\\Leftrightarrow & -175x \color{red}{+10} \color{blue}{-10} \color{blue}{+28x} & = & \color{red}{-28x} +2 \color{blue}{+28x} \color{blue}{-10} \\\Leftrightarrow & -175x+28x& = & 2-10 \\\Leftrightarrow & \color{red}{-147} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-147} & & \\\Leftrightarrow & x = \frac{8}{147} & & \\ & V = \left\{ \frac{8}{147} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 10x+\frac{20}{11}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+60} & = & \color{red}{-231x} +55 \\\Leftrightarrow & 330x \color{red}{+60} \color{blue}{-60} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{-60} \\\Leftrightarrow & 330x+231x& = & 55-60 \\\Leftrightarrow & \color{red}{561} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{561} & & \\ & V = \left\{ \frac{-5}{561} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{21}{10}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-350}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -350x \color{red}{+21} & = & \color{red}{-40x} +12 \\\Leftrightarrow & -350x \color{red}{+21} \color{blue}{-21} \color{blue}{+40x} & = & \color{red}{-40x} +12 \color{blue}{+40x} \color{blue}{-21} \\\Leftrightarrow & -350x+40x& = & 12-21 \\\Leftrightarrow & \color{red}{-310} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-310} & & \\\Leftrightarrow & x = \frac{9}{310} & & \\ & V = \left\{ \frac{9}{310} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{12}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-132} & = & \color{red}{231x} +42 \\\Leftrightarrow & 616x \color{red}{-132} \color{blue}{+132} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{+132} \\\Leftrightarrow & 616x-231x& = & 42+132 \\\Leftrightarrow & \color{red}{385} x& = & 174 \\\Leftrightarrow & x = \frac{174}{385} & & \\ & V = \left\{ \frac{174}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-48} \\\Leftrightarrow & 336x+147x& = & 14-48 \\\Leftrightarrow & \color{red}{483} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{483} & & \\ & V = \left\{ \frac{-34}{483} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -8x+\frac{9}{10} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{630}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 630x \color{red}{+60} & = & \color{red}{-560x} +63 \\\Leftrightarrow & 630x \color{red}{+60} \color{blue}{-60} \color{blue}{+560x} & = & \color{red}{-560x} +63 \color{blue}{+560x} \color{blue}{-60} \\\Leftrightarrow & 630x+560x& = & 63-60 \\\Leftrightarrow & \color{red}{1190} x& = & 3 \\\Leftrightarrow & x = \frac{3}{1190} & & \\ & V = \left\{ \frac{3}{1190} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{55x} +9 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +9 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & 198x-55x& = & 9+18 \\\Leftrightarrow & \color{red}{143} x& = & 27 \\\Leftrightarrow & x = \frac{27}{143} & & \\ & V = \left\{ \frac{27}{143} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+72} & = & \color{red}{75x} +10 \\\Leftrightarrow & -360x \color{red}{+72} \color{blue}{-72} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-72} \\\Leftrightarrow & -360x-75x& = & 10-72 \\\Leftrightarrow & \color{red}{-435} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-435} & & \\\Leftrightarrow & x = \frac{62}{435} & & \\ & V = \left\{ \frac{62}{435} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{9})& = & 6x+\frac{5}{3} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 6x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{-20} & = & \color{red}{54x} +15 \\\Leftrightarrow & -225x \color{red}{-20} \color{blue}{+20} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{+20} \\\Leftrightarrow & -225x-54x& = & 15+20 \\\Leftrightarrow & \color{red}{-279} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-279} & & \\\Leftrightarrow & x = \frac{-35}{279} & & \\ & V = \left\{ \frac{-35}{279} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{7})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+30} & = & \color{red}{168x} +28 \\\Leftrightarrow & -315x \color{red}{+30} \color{blue}{-30} \color{blue}{-168x} & = & \color{red}{168x} +28 \color{blue}{-168x} \color{blue}{-30} \\\Leftrightarrow & -315x-168x& = & 28-30 \\\Leftrightarrow & \color{red}{-483} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-483} & & \\\Leftrightarrow & x = \frac{2}{483} & & \\ & V = \left\{ \frac{2}{483} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{264x} +64 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{-264x} & = & \color{red}{264x} +64 \color{blue}{-264x} \color{blue}{+231} \\\Leftrightarrow & -1232x-264x& = & 64+231 \\\Leftrightarrow & \color{red}{-1496} x& = & 295 \\\Leftrightarrow & x = \frac{295}{-1496} & & \\\Leftrightarrow & x = \frac{-295}{1496} & & \\ & V = \left\{ \frac{-295}{1496} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -112x+49x& = & 4+20 \\\Leftrightarrow & \color{red}{-63} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-63} & & \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)