Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{-189} & = & \color{red}{-216x} +80 \\\Leftrightarrow & 1008x \color{red}{-189} \color{blue}{+189} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{+189} \\\Leftrightarrow & 1008x+216x& = & 80+189 \\\Leftrightarrow & \color{red}{1224} x& = & 269 \\\Leftrightarrow & x = \frac{269}{1224} & & \\ & V = \left\{ \frac{269}{1224} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{45x} +15 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +15 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 54x-45x& = & 15+4 \\\Leftrightarrow & \color{red}{9} x& = & 19 \\\Leftrightarrow & x = \frac{19}{9} & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{18}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+126} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 420x \color{red}{+126} \color{blue}{-126} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-126} \\\Leftrightarrow & 420x+175x& = & 15-126 \\\Leftrightarrow & \color{red}{595} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{595} & & \\ & V = \left\{ \frac{-111}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-4} & = & \color{red}{45x} +8 \\\Leftrightarrow & 40x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 40x-45x& = & 8+4 \\\Leftrightarrow & \color{red}{-5} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-5} & & \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{5})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 14x-\frac{28}{5}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-308} & = & \color{red}{495x} +20 \\\Leftrightarrow & 770x \color{red}{-308} \color{blue}{+308} \color{blue}{-495x} & = & \color{red}{495x} +20 \color{blue}{-495x} \color{blue}{+308} \\\Leftrightarrow & 770x-495x& = & 20+308 \\\Leftrightarrow & \color{red}{275} x& = & 328 \\\Leftrightarrow & x = \frac{328}{275} & & \\ & V = \left\{ \frac{328}{275} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -6x+\frac{7}{4} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -6x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-48}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{+21} & = & \color{red}{-48x} +14 \\\Leftrightarrow & -280x \color{red}{+21} \color{blue}{-21} \color{blue}{+48x} & = & \color{red}{-48x} +14 \color{blue}{+48x} \color{blue}{-21} \\\Leftrightarrow & -280x+48x& = & 14-21 \\\Leftrightarrow & \color{red}{-232} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-232} & & \\\Leftrightarrow & x = \frac{7}{232} & & \\ & V = \left\{ \frac{7}{232} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{3})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+200} & = & \color{red}{-210x} +9 \\\Leftrightarrow & 600x \color{red}{+200} \color{blue}{-200} \color{blue}{+210x} & = & \color{red}{-210x} +9 \color{blue}{+210x} \color{blue}{-200} \\\Leftrightarrow & 600x+210x& = & 9-200 \\\Leftrightarrow & \color{red}{810} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{810} & & \\ & V = \left\{ \frac{-191}{810} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{-567x} +90 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{+567x} & = & \color{red}{-567x} +90 \color{blue}{+567x} \color{blue}{-56} \\\Leftrightarrow & -252x+567x& = & 90-56 \\\Leftrightarrow & \color{red}{315} x& = & 34 \\\Leftrightarrow & x = \frac{34}{315} & & \\ & V = \left\{ \frac{34}{315} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{12})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -28x-\frac{35}{12}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{-35} & = & \color{red}{-108x} +27 \\\Leftrightarrow & -336x \color{red}{-35} \color{blue}{+35} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+35} \\\Leftrightarrow & -336x+108x& = & 27+35 \\\Leftrightarrow & \color{red}{-228} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-228} & & \\\Leftrightarrow & x = \frac{-31}{114} & & \\ & V = \left\{ \frac{-31}{114} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{9})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{10}{9}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-10} & = & \color{red}{63x} +12 \\\Leftrightarrow & 90x \color{red}{-10} \color{blue}{+10} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+10} \\\Leftrightarrow & 90x-63x& = & 12+10 \\\Leftrightarrow & \color{red}{27} x& = & 22 \\\Leftrightarrow & x = \frac{22}{27} & & \\ & V = \left\{ \frac{22}{27} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{5})& = & -2x+\frac{7}{9} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -2x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+126} & = & \color{red}{-90x} +35 \\\Leftrightarrow & 945x \color{red}{+126} \color{blue}{-126} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{-126} \\\Leftrightarrow & 945x+90x& = & 35-126 \\\Leftrightarrow & \color{red}{1035} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{1035} & & \\ & V = \left\{ \frac{-91}{1035} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-45x} +10 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{+36} \\\Leftrightarrow & -120x+45x& = & 10+36 \\\Leftrightarrow & \color{red}{-75} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-75} & & \\\Leftrightarrow & x = \frac{-46}{75} & & \\ & V = \left\{ \frac{-46}{75} \right\} & \\\end{align}\)