Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{9})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-28} & = & \color{red}{189x} +90 \\\Leftrightarrow & 504x \color{red}{-28} \color{blue}{+28} \color{blue}{-189x} & = & \color{red}{189x} +90 \color{blue}{-189x} \color{blue}{+28} \\\Leftrightarrow & 504x-189x& = & 90+28 \\\Leftrightarrow & \color{red}{315} x& = & 118 \\\Leftrightarrow & x = \frac{118}{315} & & \\ & V = \left\{ \frac{118}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{3})& = & 8x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{28}{3}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-112} & = & \color{red}{96x} +9 \\\Leftrightarrow & 252x \color{red}{-112} \color{blue}{+112} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{+112} \\\Leftrightarrow & 252x-96x& = & 9+112 \\\Leftrightarrow & \color{red}{156} x& = & 121 \\\Leftrightarrow & x = \frac{121}{156} & & \\ & V = \left\{ \frac{121}{156} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{3})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{99x} +18 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-99x} & = & \color{red}{99x} +18 \color{blue}{-99x} \color{blue}{+154} \\\Leftrightarrow & 1155x-99x& = & 18+154 \\\Leftrightarrow & \color{red}{1056} x& = & 172 \\\Leftrightarrow & x = \frac{172}{1056} & & \\\Leftrightarrow & x = \frac{43}{264} & & \\ & V = \left\{ \frac{43}{264} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{8})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x+ \frac{75}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{168x} +10 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{-168x} & = & \color{red}{168x} +10 \color{blue}{-168x} \color{blue}{-75} \\\Leftrightarrow & 480x-168x& = & 10-75 \\\Leftrightarrow & \color{red}{312} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{312} & & \\\Leftrightarrow & x = \frac{-5}{24} & & \\ & V = \left\{ \frac{-5}{24} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & 3x+\frac{5}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{63x} +35 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +35 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & 336x-63x& = & 35-60 \\\Leftrightarrow & \color{red}{273} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{273} & & \\ & V = \left\{ \frac{-25}{273} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 20x-\frac{10}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-50} & = & \color{red}{-245x} +56 \\\Leftrightarrow & 700x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & 700x+245x& = & 56+50 \\\Leftrightarrow & \color{red}{945} x& = & 106 \\\Leftrightarrow & x = \frac{106}{945} & & \\ & V = \left\{ \frac{106}{945} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{10}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-10} & = & \color{red}{21x} +10 \\\Leftrightarrow & 24x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 24x-21x& = & 10+10 \\\Leftrightarrow & \color{red}{3} x& = & 20 \\\Leftrightarrow & x = \frac{20}{3} & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{2})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -20x+\frac{25}{2}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+225} & = & \color{red}{126x} +14 \\\Leftrightarrow & -360x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +14 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & -360x-126x& = & 14-225 \\\Leftrightarrow & \color{red}{-486} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{-486} & & \\\Leftrightarrow & x = \frac{211}{486} & & \\ & V = \left\{ \frac{211}{486} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{6})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x-\frac{35}{6}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-35} & = & \color{red}{-48x} +4 \\\Leftrightarrow & 126x \color{red}{-35} \color{blue}{+35} \color{blue}{+48x} & = & \color{red}{-48x} +4 \color{blue}{+48x} \color{blue}{+35} \\\Leftrightarrow & 126x+48x& = & 4+35 \\\Leftrightarrow & \color{red}{174} x& = & 39 \\\Leftrightarrow & x = \frac{39}{174} & & \\\Leftrightarrow & x = \frac{13}{58} & & \\ & V = \left\{ \frac{13}{58} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{7})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 16x-\frac{8}{7}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{72}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-72} & = & \color{red}{-567x} +70 \\\Leftrightarrow & 1008x \color{red}{-72} \color{blue}{+72} \color{blue}{+567x} & = & \color{red}{-567x} +70 \color{blue}{+567x} \color{blue}{+72} \\\Leftrightarrow & 1008x+567x& = & 70+72 \\\Leftrightarrow & \color{red}{1575} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1575} & & \\ & V = \left\{ \frac{142}{1575} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & -6x+\frac{8}{9} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -6x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{-60} & = & \color{red}{-54x} +8 \\\Leftrightarrow & 225x \color{red}{-60} \color{blue}{+60} \color{blue}{+54x} & = & \color{red}{-54x} +8 \color{blue}{+54x} \color{blue}{+60} \\\Leftrightarrow & 225x+54x& = & 8+60 \\\Leftrightarrow & \color{red}{279} x& = & 68 \\\Leftrightarrow & x = \frac{68}{279} & & \\ & V = \left\{ \frac{68}{279} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{5})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 28x+\frac{28}{5}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{980}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 980x \color{red}{+196} & = & \color{red}{-315x} +40 \\\Leftrightarrow & 980x \color{red}{+196} \color{blue}{-196} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-196} \\\Leftrightarrow & 980x+315x& = & 40-196 \\\Leftrightarrow & \color{red}{1295} x& = & -156 \\\Leftrightarrow & x = \frac{-156}{1295} & & \\ & V = \left\{ \frac{-156}{1295} \right\} & \\\end{align}\)