Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{3})& = & -9x+\frac{5}{9} \\\Leftrightarrow & -28x+\frac{28}{3}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+84} & = & \color{red}{-81x} +5 \\\Leftrightarrow & -252x \color{red}{+84} \color{blue}{-84} \color{blue}{+81x} & = & \color{red}{-81x} +5 \color{blue}{+81x} \color{blue}{-84} \\\Leftrightarrow & -252x+81x& = & 5-84 \\\Leftrightarrow & \color{red}{-171} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-171} & & \\\Leftrightarrow & x = \frac{79}{171} & & \\ & V = \left\{ \frac{79}{171} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-108} & = & \color{red}{495x} +44 \\\Leftrightarrow & -1188x \color{red}{-108} \color{blue}{+108} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{+108} \\\Leftrightarrow & -1188x-495x& = & 44+108 \\\Leftrightarrow & \color{red}{-1683} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1683} & & \\\Leftrightarrow & x = \frac{-152}{1683} & & \\ & V = \left\{ \frac{-152}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-480}{ \color{blue}{20} }x- \frac{72}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -480x \color{red}{-72} & = & \color{red}{140x} +35 \\\Leftrightarrow & -480x \color{red}{-72} \color{blue}{+72} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+72} \\\Leftrightarrow & -480x-140x& = & 35+72 \\\Leftrightarrow & \color{red}{-620} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-620} & & \\\Leftrightarrow & x = \frac{-107}{620} & & \\ & V = \left\{ \frac{-107}{620} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-56} & = & \color{red}{567x} +81 \\\Leftrightarrow & -1260x \color{red}{-56} \color{blue}{+56} \color{blue}{-567x} & = & \color{red}{567x} +81 \color{blue}{-567x} \color{blue}{+56} \\\Leftrightarrow & -1260x-567x& = & 81+56 \\\Leftrightarrow & \color{red}{-1827} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-1827} & & \\\Leftrightarrow & x = \frac{-137}{1827} & & \\ & V = \left\{ \frac{-137}{1827} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{-55x} +3 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{+55x} & = & \color{red}{-55x} +3 \color{blue}{+55x} \color{blue}{-30} \\\Leftrightarrow & 198x+55x& = & 3-30 \\\Leftrightarrow & \color{red}{253} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{253} & & \\ & V = \left\{ \frac{-27}{253} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{231x} +22 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & 396x-231x& = & 22-54 \\\Leftrightarrow & \color{red}{165} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{165} & & \\ & V = \left\{ \frac{-32}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{7})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{20}{7}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-60} & = & \color{red}{-168x} +14 \\\Leftrightarrow & -315x \color{red}{-60} \color{blue}{+60} \color{blue}{+168x} & = & \color{red}{-168x} +14 \color{blue}{+168x} \color{blue}{+60} \\\Leftrightarrow & -315x+168x& = & 14+60 \\\Leftrightarrow & \color{red}{-147} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-147} & & \\\Leftrightarrow & x = \frac{-74}{147} & & \\ & V = \left\{ \frac{-74}{147} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{-270} & = & \color{red}{315x} +56 \\\Leftrightarrow & 1134x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & 1134x-315x& = & 56+270 \\\Leftrightarrow & \color{red}{819} x& = & 326 \\\Leftrightarrow & x = \frac{326}{819} & & \\ & V = \left\{ \frac{326}{819} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{+24} & = & \color{red}{70x} +3 \\\Leftrightarrow & -160x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -160x-70x& = & 3-24 \\\Leftrightarrow & \color{red}{-230} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-230} & & \\\Leftrightarrow & x = \frac{21}{230} & & \\ & V = \left\{ \frac{21}{230} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+54} & = & \color{red}{567x} +14 \\\Leftrightarrow & 630x \color{red}{+54} \color{blue}{-54} \color{blue}{-567x} & = & \color{red}{567x} +14 \color{blue}{-567x} \color{blue}{-54} \\\Leftrightarrow & 630x-567x& = & 14-54 \\\Leftrightarrow & \color{red}{63} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{63} & & \\ & V = \left\{ \frac{-40}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & 990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 990x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{759} x& = & 164 \\\Leftrightarrow & x = \frac{164}{759} & & \\ & V = \left\{ \frac{164}{759} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-6} \\\Leftrightarrow & 30x+25x& = & 6-6 \\\Leftrightarrow & \color{red}{55} x& = & 0 \\\Leftrightarrow & x = \frac{0}{55} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)