Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -4x-\frac{4}{3}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{-189x} +9 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{+189x} & = & \color{red}{-189x} +9 \color{blue}{+189x} \color{blue}{+28} \\\Leftrightarrow & -84x+189x& = & 9+28 \\\Leftrightarrow & \color{red}{105} x& = & 37 \\\Leftrightarrow & x = \frac{37}{105} & & \\ & V = \left\{ \frac{37}{105} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 30x+\frac{12}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+84} & = & \color{red}{539x} +99 \\\Leftrightarrow & 2310x \color{red}{+84} \color{blue}{-84} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-84} \\\Leftrightarrow & 2310x-539x& = & 99-84 \\\Leftrightarrow & \color{red}{1771} x& = & 15 \\\Leftrightarrow & x = \frac{15}{1771} & & \\ & V = \left\{ \frac{15}{1771} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+18} & = & \color{red}{55x} +8 \\\Leftrightarrow & 198x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 198x-55x& = & 8-18 \\\Leftrightarrow & \color{red}{143} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{143} & & \\ & V = \left\{ \frac{-10}{143} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{7})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{20}{7}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+160} & = & \color{red}{504x} +49 \\\Leftrightarrow & 560x \color{red}{+160} \color{blue}{-160} \color{blue}{-504x} & = & \color{red}{504x} +49 \color{blue}{-504x} \color{blue}{-160} \\\Leftrightarrow & 560x-504x& = & 49-160 \\\Leftrightarrow & \color{red}{56} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{56} & & \\ & V = \left\{ \frac{-111}{56} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{6}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-66} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 660x \color{red}{-66} \color{blue}{+66} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+66} \\\Leftrightarrow & 660x+275x& = & 10+66 \\\Leftrightarrow & \color{red}{935} x& = & 76 \\\Leftrightarrow & x = \frac{76}{935} & & \\ & V = \left\{ \frac{76}{935} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & -3x+\frac{5}{12} \\\Leftrightarrow & -8x-\frac{6}{5}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-480}{ \color{blue}{60} }x- \frac{72}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -480x \color{red}{-72} & = & \color{red}{-180x} +25 \\\Leftrightarrow & -480x \color{red}{-72} \color{blue}{+72} \color{blue}{+180x} & = & \color{red}{-180x} +25 \color{blue}{+180x} \color{blue}{+72} \\\Leftrightarrow & -480x+180x& = & 25+72 \\\Leftrightarrow & \color{red}{-300} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-300} & & \\\Leftrightarrow & x = \frac{-97}{300} & & \\ & V = \left\{ \frac{-97}{300} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{50x} +9 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+12} \\\Leftrightarrow & 60x-50x& = & 9+12 \\\Leftrightarrow & \color{red}{10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{10} & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{8}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+40} & = & \color{red}{105x} +18 \\\Leftrightarrow & -150x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & -150x-105x& = & 18-40 \\\Leftrightarrow & \color{red}{-255} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-255} & & \\\Leftrightarrow & x = \frac{22}{255} & & \\ & V = \left\{ \frac{22}{255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -6x-\frac{12}{11}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-60} & = & \color{red}{-385x} +99 \\\Leftrightarrow & -330x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & -330x+385x& = & 99+60 \\\Leftrightarrow & \color{red}{55} x& = & 159 \\\Leftrightarrow & x = \frac{159}{55} & & \\ & V = \left\{ \frac{159}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{20}{11}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+100} & = & \color{red}{-440x} +66 \\\Leftrightarrow & -825x \color{red}{+100} \color{blue}{-100} \color{blue}{+440x} & = & \color{red}{-440x} +66 \color{blue}{+440x} \color{blue}{-100} \\\Leftrightarrow & -825x+440x& = & 66-100 \\\Leftrightarrow & \color{red}{-385} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-385} & & \\\Leftrightarrow & x = \frac{34}{385} & & \\ & V = \left\{ \frac{34}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 14x+\frac{14}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1260}{ \color{blue}{90} }x+ \frac{140}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1260x \color{red}{+140} & = & \color{red}{810x} +27 \\\Leftrightarrow & 1260x \color{red}{+140} \color{blue}{-140} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{-140} \\\Leftrightarrow & 1260x-810x& = & 27-140 \\\Leftrightarrow & \color{red}{450} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{450} & & \\ & V = \left\{ \frac{-113}{450} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{12}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+84} & = & \color{red}{385x} +44 \\\Leftrightarrow & 693x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & 693x-385x& = & 44-84 \\\Leftrightarrow & \color{red}{308} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{308} & & \\\Leftrightarrow & x = \frac{-10}{77} & & \\ & V = \left\{ \frac{-10}{77} \right\} & \\\end{align}\)