Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{7})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{20}{7}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+60} & = & \color{red}{63x} +70 \\\Leftrightarrow & 168x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +70 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & 168x-63x& = & 70-60 \\\Leftrightarrow & \color{red}{105} x& = & 10 \\\Leftrightarrow & x = \frac{10}{105} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{16}{11}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{144}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-144} & = & \color{red}{891x} +110 \\\Leftrightarrow & -792x \color{red}{-144} \color{blue}{+144} \color{blue}{-891x} & = & \color{red}{891x} +110 \color{blue}{-891x} \color{blue}{+144} \\\Leftrightarrow & -792x-891x& = & 110+144 \\\Leftrightarrow & \color{red}{-1683} x& = & 254 \\\Leftrightarrow & x = \frac{254}{-1683} & & \\\Leftrightarrow & x = \frac{-254}{1683} & & \\ & V = \left\{ \frac{-254}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{1}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{7}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{49}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-49} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 588x \color{red}{-49} \color{blue}{+49} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+49} \\\Leftrightarrow & 588x+63x& = & 30+49 \\\Leftrightarrow & \color{red}{651} x& = & 79 \\\Leftrightarrow & x = \frac{79}{651} & & \\ & V = \left\{ \frac{79}{651} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & 420x-175x& = & 42-30 \\\Leftrightarrow & \color{red}{245} x& = & 12 \\\Leftrightarrow & x = \frac{12}{245} & & \\ & V = \left\{ \frac{12}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 25x+\frac{15}{11}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{+15} & = & \color{red}{22x} +6 \\\Leftrightarrow & 275x \color{red}{+15} \color{blue}{-15} \color{blue}{-22x} & = & \color{red}{22x} +6 \color{blue}{-22x} \color{blue}{-15} \\\Leftrightarrow & 275x-22x& = & 6-15 \\\Leftrightarrow & \color{red}{253} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{253} & & \\ & V = \left\{ \frac{-9}{253} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & 2x+\frac{5}{4} \\\Leftrightarrow & 21x+\frac{21}{2}& = & 2x+\frac{5}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x+ \frac{42}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{+42} & = & \color{red}{8x} +5 \\\Leftrightarrow & 84x \color{red}{+42} \color{blue}{-42} \color{blue}{-8x} & = & \color{red}{8x} +5 \color{blue}{-8x} \color{blue}{-42} \\\Leftrightarrow & 84x-8x& = & 5-42 \\\Leftrightarrow & \color{red}{76} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{76} & & \\ & V = \left\{ \frac{-37}{76} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+168} & = & \color{red}{385x} +88 \\\Leftrightarrow & 1848x \color{red}{+168} \color{blue}{-168} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{-168} \\\Leftrightarrow & 1848x-385x& = & 88-168 \\\Leftrightarrow & \color{red}{1463} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{1463} & & \\ & V = \left\{ \frac{-80}{1463} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-88} & = & \color{red}{-297x} +54 \\\Leftrightarrow & 792x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & 792x+297x& = & 54+88 \\\Leftrightarrow & \color{red}{1089} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1089} & & \\ & V = \left\{ \frac{142}{1089} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -24x+\frac{12}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{+120} & = & \color{red}{550x} +33 \\\Leftrightarrow & -2640x \color{red}{+120} \color{blue}{-120} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{-120} \\\Leftrightarrow & -2640x-550x& = & 33-120 \\\Leftrightarrow & \color{red}{-3190} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-3190} & & \\\Leftrightarrow & x = \frac{3}{110} & & \\ & V = \left\{ \frac{3}{110} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-36} \\\Leftrightarrow & 360x+225x& = & 50-36 \\\Leftrightarrow & \color{red}{585} x& = & 14 \\\Leftrightarrow & x = \frac{14}{585} & & \\ & V = \left\{ \frac{14}{585} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{9})& = & 4x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+80} & = & \color{red}{144x} +27 \\\Leftrightarrow & 540x \color{red}{+80} \color{blue}{-80} \color{blue}{-144x} & = & \color{red}{144x} +27 \color{blue}{-144x} \color{blue}{-80} \\\Leftrightarrow & 540x-144x& = & 27-80 \\\Leftrightarrow & \color{red}{396} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{396} & & \\ & V = \left\{ \frac{-53}{396} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{-18} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -264x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & -264x+55x& = & 6+18 \\\Leftrightarrow & \color{red}{-209} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-209} & & \\\Leftrightarrow & x = \frac{-24}{209} & & \\ & V = \left\{ \frac{-24}{209} \right\} & \\\end{align}\)