Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{8}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+24} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -396x \color{red}{+24} \color{blue}{-24} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-24} \\\Leftrightarrow & -396x+165x& = & 44-24 \\\Leftrightarrow & \color{red}{-231} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-231} & & \\\Leftrightarrow & x = \frac{-20}{231} & & \\ & V = \left\{ \frac{-20}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{9}{7}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1008}{ \color{blue}{84} }x- \frac{108}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1008x \color{red}{-108} & = & \color{red}{-420x} +35 \\\Leftrightarrow & -1008x \color{red}{-108} \color{blue}{+108} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{+108} \\\Leftrightarrow & -1008x+420x& = & 35+108 \\\Leftrightarrow & \color{red}{-588} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-588} & & \\\Leftrightarrow & x = \frac{-143}{588} & & \\ & V = \left\{ \frac{-143}{588} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & -6x+\frac{6}{7} \\\Leftrightarrow & -28x-\frac{28}{3}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-196} & = & \color{red}{-126x} +18 \\\Leftrightarrow & -588x \color{red}{-196} \color{blue}{+196} \color{blue}{+126x} & = & \color{red}{-126x} +18 \color{blue}{+126x} \color{blue}{+196} \\\Leftrightarrow & -588x+126x& = & 18+196 \\\Leftrightarrow & \color{red}{-462} x& = & 214 \\\Leftrightarrow & x = \frac{214}{-462} & & \\\Leftrightarrow & x = \frac{-107}{231} & & \\ & V = \left\{ \frac{-107}{231} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{+10} & = & \color{red}{-44x} +6 \\\Leftrightarrow & -275x \color{red}{+10} \color{blue}{-10} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{-10} \\\Leftrightarrow & -275x+44x& = & 6-10 \\\Leftrightarrow & \color{red}{-231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-231} & & \\\Leftrightarrow & x = \frac{4}{231} & & \\ & V = \left\{ \frac{4}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-16} & = & \color{red}{49x} +6 \\\Leftrightarrow & 140x \color{red}{-16} \color{blue}{+16} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+16} \\\Leftrightarrow & 140x-49x& = & 6+16 \\\Leftrightarrow & \color{red}{91} x& = & 22 \\\Leftrightarrow & x = \frac{22}{91} & & \\ & V = \left\{ \frac{22}{91} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+270} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -1188x \color{red}{+270} \color{blue}{-270} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-270} \\\Leftrightarrow & -1188x+495x& = & 22-270 \\\Leftrightarrow & \color{red}{-693} x& = & -248 \\\Leftrightarrow & x = \frac{-248}{-693} & & \\\Leftrightarrow & x = \frac{248}{693} & & \\ & V = \left\{ \frac{248}{693} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{+90} \\\Leftrightarrow & -594x+693x& = & 22+90 \\\Leftrightarrow & \color{red}{99} x& = & 112 \\\Leftrightarrow & x = \frac{112}{99} & & \\ & V = \left\{ \frac{112}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+90} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & -660x-275x& = & 22-90 \\\Leftrightarrow & \color{red}{-935} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-935} & & \\\Leftrightarrow & x = \frac{4}{55} & & \\ & V = \left\{ \frac{4}{55} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{15}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+15} & = & \color{red}{55x} +6 \\\Leftrightarrow & 66x \color{red}{+15} \color{blue}{-15} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-15} \\\Leftrightarrow & 66x-55x& = & 6-15 \\\Leftrightarrow & \color{red}{11} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{9})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+16} & = & \color{red}{-126x} +45 \\\Leftrightarrow & -360x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & -360x+126x& = & 45-16 \\\Leftrightarrow & \color{red}{-234} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-234} & & \\\Leftrightarrow & x = \frac{-29}{234} & & \\ & V = \left\{ \frac{-29}{234} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -2x+\frac{3}{2} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-28x} +21 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+28x} & = & \color{red}{-28x} +21 \color{blue}{+28x} \color{blue}{-60} \\\Leftrightarrow & -252x+28x& = & 21-60 \\\Leftrightarrow & \color{red}{-224} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-224} & & \\\Leftrightarrow & x = \frac{39}{224} & & \\ & V = \left\{ \frac{39}{224} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{-6x} +8 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{+6x} & = & \color{red}{-6x} +8 \color{blue}{+6x} \color{blue}{+14} \\\Leftrightarrow & 105x+6x& = & 8+14 \\\Leftrightarrow & \color{red}{111} x& = & 22 \\\Leftrightarrow & x = \frac{22}{111} & & \\ & V = \left\{ \frac{22}{111} \right\} & \\\end{align}\)