Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{3})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+200} & = & \color{red}{90x} +27 \\\Leftrightarrow & 300x \color{red}{+200} \color{blue}{-200} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-200} \\\Leftrightarrow & 300x-90x& = & 27-200 \\\Leftrightarrow & \color{red}{210} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{210} & & \\ & V = \left\{ \frac{-173}{210} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & 8x+\frac{8}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{168x} +24 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{-168x} & = & \color{red}{168x} +24 \color{blue}{-168x} \color{blue}{+98} \\\Leftrightarrow & -441x-168x& = & 24+98 \\\Leftrightarrow & \color{red}{-609} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-609} & & \\\Leftrightarrow & x = \frac{-122}{609} & & \\ & V = \left\{ \frac{-122}{609} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 4x+\frac{8}{9} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{+54} & = & \color{red}{252x} +56 \\\Leftrightarrow & 567x \color{red}{+54} \color{blue}{-54} \color{blue}{-252x} & = & \color{red}{252x} +56 \color{blue}{-252x} \color{blue}{-54} \\\Leftrightarrow & 567x-252x& = & 56-54 \\\Leftrightarrow & \color{red}{315} x& = & 2 \\\Leftrightarrow & x = \frac{2}{315} & & \\ & V = \left\{ \frac{2}{315} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+264} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -2310x \color{red}{+264} \color{blue}{-264} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{-264} \\\Leftrightarrow & -2310x+539x& = & 14-264 \\\Leftrightarrow & \color{red}{-1771} x& = & -250 \\\Leftrightarrow & x = \frac{-250}{-1771} & & \\\Leftrightarrow & x = \frac{250}{1771} & & \\ & V = \left\{ \frac{250}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 21x-\frac{21}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{231}{ \color{blue}{11} }x- \frac{21}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 231x \color{red}{-21} & = & \color{red}{55x} +5 \\\Leftrightarrow & 231x \color{red}{-21} \color{blue}{+21} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+21} \\\Leftrightarrow & 231x-55x& = & 5+21 \\\Leftrightarrow & \color{red}{176} x& = & 26 \\\Leftrightarrow & x = \frac{26}{176} & & \\\Leftrightarrow & x = \frac{13}{88} & & \\ & V = \left\{ \frac{13}{88} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{12}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+12} & = & \color{red}{33x} +6 \\\Leftrightarrow & 220x \color{red}{+12} \color{blue}{-12} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{-12} \\\Leftrightarrow & 220x-33x& = & 6-12 \\\Leftrightarrow & \color{red}{187} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{187} & & \\ & V = \left\{ \frac{-6}{187} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{20}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{+27} & = & \color{red}{60x} +20 \\\Leftrightarrow & 270x \color{red}{+27} \color{blue}{-27} \color{blue}{-60x} & = & \color{red}{60x} +20 \color{blue}{-60x} \color{blue}{-27} \\\Leftrightarrow & 270x-60x& = & 20-27 \\\Leftrightarrow & \color{red}{210} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{210} & & \\\Leftrightarrow & x = \frac{-1}{30} & & \\ & V = \left\{ \frac{-1}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{8}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+32} & = & \color{red}{196x} +21 \\\Leftrightarrow & -168x \color{red}{+32} \color{blue}{-32} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-32} \\\Leftrightarrow & -168x-196x& = & 21-32 \\\Leftrightarrow & \color{red}{-364} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-364} & & \\\Leftrightarrow & x = \frac{11}{364} & & \\ & V = \left\{ \frac{11}{364} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -14x+\frac{14}{9}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x+ \frac{28}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{+28} & = & \color{red}{-54x} +15 \\\Leftrightarrow & -252x \color{red}{+28} \color{blue}{-28} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{-28} \\\Leftrightarrow & -252x+54x& = & 15-28 \\\Leftrightarrow & \color{red}{-198} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-198} & & \\\Leftrightarrow & x = \frac{13}{198} & & \\ & V = \left\{ \frac{13}{198} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-32} & = & \color{red}{-84x} +9 \\\Leftrightarrow & -120x \color{red}{-32} \color{blue}{+32} \color{blue}{+84x} & = & \color{red}{-84x} +9 \color{blue}{+84x} \color{blue}{+32} \\\Leftrightarrow & -120x+84x& = & 9+32 \\\Leftrightarrow & \color{red}{-36} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-36} & & \\\Leftrightarrow & x = \frac{-41}{36} & & \\ & V = \left\{ \frac{-41}{36} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{11})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-10} & = & \color{red}{-77x} +8 \\\Leftrightarrow & 165x \color{red}{-10} \color{blue}{+10} \color{blue}{+77x} & = & \color{red}{-77x} +8 \color{blue}{+77x} \color{blue}{+10} \\\Leftrightarrow & 165x+77x& = & 8+10 \\\Leftrightarrow & \color{red}{242} x& = & 18 \\\Leftrightarrow & x = \frac{18}{242} & & \\\Leftrightarrow & x = \frac{9}{121} & & \\ & V = \left\{ \frac{9}{121} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 180x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{105} & & \\ & V = \left\{ \frac{46}{105} \right\} & \\\end{align}\)