Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{11})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{12}{11}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-108} & = & \color{red}{792x} +110 \\\Leftrightarrow & -1485x \color{red}{-108} \color{blue}{+108} \color{blue}{-792x} & = & \color{red}{792x} +110 \color{blue}{-792x} \color{blue}{+108} \\\Leftrightarrow & -1485x-792x& = & 110+108 \\\Leftrightarrow & \color{red}{-2277} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-2277} & & \\\Leftrightarrow & x = \frac{-218}{2277} & & \\ & V = \left\{ \frac{-218}{2277} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+60} & = & \color{red}{70x} +49 \\\Leftrightarrow & 168x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 168x-70x& = & 49-60 \\\Leftrightarrow & \color{red}{98} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{98} & & \\ & V = \left\{ \frac{-11}{98} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{11})& = & 4x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{6}{11}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{+18} & = & \color{red}{132x} +22 \\\Leftrightarrow & 297x \color{red}{+18} \color{blue}{-18} \color{blue}{-132x} & = & \color{red}{132x} +22 \color{blue}{-132x} \color{blue}{-18} \\\Leftrightarrow & 297x-132x& = & 22-18 \\\Leftrightarrow & \color{red}{165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{165} & & \\ & V = \left\{ \frac{4}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-168} & = & \color{red}{-245x} +30 \\\Leftrightarrow & 840x \color{red}{-168} \color{blue}{+168} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{+168} \\\Leftrightarrow & 840x+245x& = & 30+168 \\\Leftrightarrow & \color{red}{1085} x& = & 198 \\\Leftrightarrow & x = \frac{198}{1085} & & \\ & V = \left\{ \frac{198}{1085} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{11})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 24x+\frac{30}{11}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+210} & = & \color{red}{385x} +55 \\\Leftrightarrow & 1848x \color{red}{+210} \color{blue}{-210} \color{blue}{-385x} & = & \color{red}{385x} +55 \color{blue}{-385x} \color{blue}{-210} \\\Leftrightarrow & 1848x-385x& = & 55-210 \\\Leftrightarrow & \color{red}{1463} x& = & -155 \\\Leftrightarrow & x = \frac{-155}{1463} & & \\ & V = \left\{ \frac{-155}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -24x+\frac{18}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{35x} +3 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & -120x-35x& = & 3-18 \\\Leftrightarrow & \color{red}{-155} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-155} & & \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & 3x+\frac{7}{9} \\\Leftrightarrow & -25x+\frac{20}{3}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+60} & = & \color{red}{27x} +7 \\\Leftrightarrow & -225x \color{red}{+60} \color{blue}{-60} \color{blue}{-27x} & = & \color{red}{27x} +7 \color{blue}{-27x} \color{blue}{-60} \\\Leftrightarrow & -225x-27x& = & 7-60 \\\Leftrightarrow & \color{red}{-252} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-252} & & \\\Leftrightarrow & x = \frac{53}{252} & & \\ & V = \left\{ \frac{53}{252} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{11})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{14}{11}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x+ \frac{42}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{+42} & = & \color{red}{66x} +88 \\\Leftrightarrow & 693x \color{red}{+42} \color{blue}{-42} \color{blue}{-66x} & = & \color{red}{66x} +88 \color{blue}{-66x} \color{blue}{-42} \\\Leftrightarrow & 693x-66x& = & 88-42 \\\Leftrightarrow & \color{red}{627} x& = & 46 \\\Leftrightarrow & x = \frac{46}{627} & & \\ & V = \left\{ \frac{46}{627} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{441x} +28 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+90} \\\Leftrightarrow & -630x-441x& = & 28+90 \\\Leftrightarrow & \color{red}{-1071} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-1071} & & \\\Leftrightarrow & x = \frac{-118}{1071} & & \\ & V = \left\{ \frac{-118}{1071} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{135x} +10 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{+36} \\\Leftrightarrow & -120x-135x& = & 10+36 \\\Leftrightarrow & \color{red}{-255} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-255} & & \\\Leftrightarrow & x = \frac{-46}{255} & & \\ & V = \left\{ \frac{-46}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{50x} +25 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{-18} \\\Leftrightarrow & 120x-50x& = & 25-18 \\\Leftrightarrow & \color{red}{70} x& = & 7 \\\Leftrightarrow & x = \frac{7}{70} & & \\\Leftrightarrow & x = \frac{1}{10} & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-15} & = & \color{red}{-40x} +18 \\\Leftrightarrow & -96x \color{red}{-15} \color{blue}{+15} \color{blue}{+40x} & = & \color{red}{-40x} +18 \color{blue}{+40x} \color{blue}{+15} \\\Leftrightarrow & -96x+40x& = & 18+15 \\\Leftrightarrow & \color{red}{-56} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-56} & & \\\Leftrightarrow & x = \frac{-33}{56} & & \\ & V = \left\{ \frac{-33}{56} \right\} & \\\end{align}\)