Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{9})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{16}{9}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x+ \frac{32}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{+32} & = & \color{red}{90x} +27 \\\Leftrightarrow & -216x \color{red}{+32} \color{blue}{-32} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-32} \\\Leftrightarrow & -216x-90x& = & 27-32 \\\Leftrightarrow & \color{red}{-306} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-306} & & \\\Leftrightarrow & x = \frac{5}{306} & & \\ & V = \left\{ \frac{5}{306} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{7})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{25}{7}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{225}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+225} & = & \color{red}{504x} +14 \\\Leftrightarrow & -945x \color{red}{+225} \color{blue}{-225} \color{blue}{-504x} & = & \color{red}{504x} +14 \color{blue}{-504x} \color{blue}{-225} \\\Leftrightarrow & -945x-504x& = & 14-225 \\\Leftrightarrow & \color{red}{-1449} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{-1449} & & \\\Leftrightarrow & x = \frac{211}{1449} & & \\ & V = \left\{ \frac{211}{1449} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{70x} +49 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 252x-70x& = & 49-60 \\\Leftrightarrow & \color{red}{182} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{182} & & \\ & V = \left\{ \frac{-11}{182} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{6})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x+\frac{25}{6}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1320}{ \color{blue}{66} }x+ \frac{275}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{12}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1320x \color{red}{+275} & = & \color{red}{-462x} +12 \\\Leftrightarrow & -1320x \color{red}{+275} \color{blue}{-275} \color{blue}{+462x} & = & \color{red}{-462x} +12 \color{blue}{+462x} \color{blue}{-275} \\\Leftrightarrow & -1320x+462x& = & 12-275 \\\Leftrightarrow & \color{red}{-858} x& = & -263 \\\Leftrightarrow & x = \frac{-263}{-858} & & \\\Leftrightarrow & x = \frac{263}{858} & & \\ & V = \left\{ \frac{263}{858} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+10} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -70x+49x& = & 9-10 \\\Leftrightarrow & \color{red}{-21} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-21} & & \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{96x} +9 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{-56} \\\Leftrightarrow & -252x-96x& = & 9-56 \\\Leftrightarrow & \color{red}{-348} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-348} & & \\\Leftrightarrow & x = \frac{47}{348} & & \\ & V = \left\{ \frac{47}{348} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{990x} +99 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-990x} & = & \color{red}{990x} +99 \color{blue}{-990x} \color{blue}{+180} \\\Leftrightarrow & -1980x-990x& = & 99+180 \\\Leftrightarrow & \color{red}{-2970} x& = & 279 \\\Leftrightarrow & x = \frac{279}{-2970} & & \\\Leftrightarrow & x = \frac{-31}{330} & & \\ & V = \left\{ \frac{-31}{330} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{+100} & = & \color{red}{-490x} +21 \\\Leftrightarrow & -420x \color{red}{+100} \color{blue}{-100} \color{blue}{+490x} & = & \color{red}{-490x} +21 \color{blue}{+490x} \color{blue}{-100} \\\Leftrightarrow & -420x+490x& = & 21-100 \\\Leftrightarrow & \color{red}{70} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{70} & & \\ & V = \left\{ \frac{-79}{70} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{2})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -21x+\frac{21}{2}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x+ \frac{231}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{+231} & = & \color{red}{176x} +10 \\\Leftrightarrow & -462x \color{red}{+231} \color{blue}{-231} \color{blue}{-176x} & = & \color{red}{176x} +10 \color{blue}{-176x} \color{blue}{-231} \\\Leftrightarrow & -462x-176x& = & 10-231 \\\Leftrightarrow & \color{red}{-638} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-638} & & \\\Leftrightarrow & x = \frac{221}{638} & & \\ & V = \left\{ \frac{221}{638} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 4x+\frac{3}{10} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{630}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{280}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 630x \color{red}{+60} & = & \color{red}{280x} +21 \\\Leftrightarrow & 630x \color{red}{+60} \color{blue}{-60} \color{blue}{-280x} & = & \color{red}{280x} +21 \color{blue}{-280x} \color{blue}{-60} \\\Leftrightarrow & 630x-280x& = & 21-60 \\\Leftrightarrow & \color{red}{350} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{350} & & \\ & V = \left\{ \frac{-39}{350} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{224}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 224x \color{red}{+48} & = & \color{red}{-168x} +21 \\\Leftrightarrow & 224x \color{red}{+48} \color{blue}{-48} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{-48} \\\Leftrightarrow & 224x+168x& = & 21-48 \\\Leftrightarrow & \color{red}{392} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{392} & & \\ & V = \left\{ \frac{-27}{392} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+220} & = & \color{red}{539x} +42 \\\Leftrightarrow & -1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -1540x-539x& = & 42-220 \\\Leftrightarrow & \color{red}{-2079} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{-2079} & & \\\Leftrightarrow & x = \frac{178}{2079} & & \\ & V = \left\{ \frac{178}{2079} \right\} & \\\end{align}\)