Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{3})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{189x} +9 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +9 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & 168x-189x& = & 9-56 \\\Leftrightarrow & \color{red}{-21} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-21} & & \\\Leftrightarrow & x = \frac{47}{21} & & \\ & V = \left\{ \frac{47}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1750}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1750x \color{red}{+100} & = & \color{red}{-630x} +63 \\\Leftrightarrow & -1750x \color{red}{+100} \color{blue}{-100} \color{blue}{+630x} & = & \color{red}{-630x} +63 \color{blue}{+630x} \color{blue}{-100} \\\Leftrightarrow & -1750x+630x& = & 63-100 \\\Leftrightarrow & \color{red}{-1120} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-1120} & & \\\Leftrightarrow & x = \frac{37}{1120} & & \\ & V = \left\{ \frac{37}{1120} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{15}{2}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+105} & = & \color{red}{98x} +18 \\\Leftrightarrow & -84x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +18 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & -84x-98x& = & 18-105 \\\Leftrightarrow & \color{red}{-182} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-182} & & \\\Leftrightarrow & x = \frac{87}{182} & & \\ & V = \left\{ \frac{87}{182} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{3})& = & 3x+\frac{9}{5} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{45x} +27 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{-45x} & = & \color{red}{45x} +27 \color{blue}{-45x} \color{blue}{-70} \\\Leftrightarrow & -210x-45x& = & 27-70 \\\Leftrightarrow & \color{red}{-255} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-255} & & \\\Leftrightarrow & x = \frac{43}{255} & & \\ & V = \left\{ \frac{43}{255} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-88} & = & \color{red}{297x} +90 \\\Leftrightarrow & 1584x \color{red}{-88} \color{blue}{+88} \color{blue}{-297x} & = & \color{red}{297x} +90 \color{blue}{-297x} \color{blue}{+88} \\\Leftrightarrow & 1584x-297x& = & 90+88 \\\Leftrightarrow & \color{red}{1287} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1287} & & \\ & V = \left\{ \frac{178}{1287} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{6}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+42} & = & \color{red}{245x} +50 \\\Leftrightarrow & 525x \color{red}{+42} \color{blue}{-42} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-42} \\\Leftrightarrow & 525x-245x& = & 50-42 \\\Leftrightarrow & \color{red}{280} x& = & 8 \\\Leftrightarrow & x = \frac{8}{280} & & \\\Leftrightarrow & x = \frac{1}{35} & & \\ & V = \left\{ \frac{1}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{10})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{9}{10}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+99} & = & \color{red}{550x} +60 \\\Leftrightarrow & 1320x \color{red}{+99} \color{blue}{-99} \color{blue}{-550x} & = & \color{red}{550x} +60 \color{blue}{-550x} \color{blue}{-99} \\\Leftrightarrow & 1320x-550x& = & 60-99 \\\Leftrightarrow & \color{red}{770} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{770} & & \\ & V = \left\{ \frac{-39}{770} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{10}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+50} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 440x \color{red}{+50} \color{blue}{-50} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-50} \\\Leftrightarrow & 440x+275x& = & 66-50 \\\Leftrightarrow & \color{red}{715} x& = & 16 \\\Leftrightarrow & x = \frac{16}{715} & & \\ & V = \left\{ \frac{16}{715} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{7}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{96x} +7 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +7 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -180x-96x& = & 7-45 \\\Leftrightarrow & \color{red}{-276} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-276} & & \\\Leftrightarrow & x = \frac{19}{138} & & \\ & V = \left\{ \frac{19}{138} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{165x} +30 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & 880x-165x& = & 30+132 \\\Leftrightarrow & \color{red}{715} x& = & 162 \\\Leftrightarrow & x = \frac{162}{715} & & \\ & V = \left\{ \frac{162}{715} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{12}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+60} & = & \color{red}{245x} +42 \\\Leftrightarrow & -210x \color{red}{+60} \color{blue}{-60} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-60} \\\Leftrightarrow & -210x-245x& = & 42-60 \\\Leftrightarrow & \color{red}{-455} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-455} & & \\\Leftrightarrow & x = \frac{18}{455} & & \\ & V = \left\{ \frac{18}{455} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{11})& = & 4x+\frac{4}{11} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{+35} & = & \color{red}{44x} +4 \\\Leftrightarrow & -385x \color{red}{+35} \color{blue}{-35} \color{blue}{-44x} & = & \color{red}{44x} +4 \color{blue}{-44x} \color{blue}{-35} \\\Leftrightarrow & -385x-44x& = & 4-35 \\\Leftrightarrow & \color{red}{-429} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-429} & & \\\Leftrightarrow & x = \frac{31}{429} & & \\ & V = \left\{ \frac{31}{429} \right\} & \\\end{align}\)