Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 28x-\frac{28}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-196} & = & \color{red}{63x} +6 \\\Leftrightarrow & 588x \color{red}{-196} \color{blue}{+196} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+196} \\\Leftrightarrow & 588x-63x& = & 6+196 \\\Leftrightarrow & \color{red}{525} x& = & 202 \\\Leftrightarrow & x = \frac{202}{525} & & \\ & V = \left\{ \frac{202}{525} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 2x+\frac{5}{9} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 2x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+108} & = & \color{red}{90x} +25 \\\Leftrightarrow & -810x \color{red}{+108} \color{blue}{-108} \color{blue}{-90x} & = & \color{red}{90x} +25 \color{blue}{-90x} \color{blue}{-108} \\\Leftrightarrow & -810x-90x& = & 25-108 \\\Leftrightarrow & \color{red}{-900} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-900} & & \\\Leftrightarrow & x = \frac{83}{900} & & \\ & V = \left\{ \frac{83}{900} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{-245x} +56 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -350x+245x& = & 56-50 \\\Leftrightarrow & \color{red}{-105} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-105} & & \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-20} & = & \color{red}{35x} +3 \\\Leftrightarrow & -175x \color{red}{-20} \color{blue}{+20} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+20} \\\Leftrightarrow & -175x-35x& = & 3+20 \\\Leftrightarrow & \color{red}{-210} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-210} & & \\\Leftrightarrow & x = \frac{-23}{210} & & \\ & V = \left\{ \frac{-23}{210} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -2x+\frac{3}{10} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+105} & = & \color{red}{-80x} +12 \\\Leftrightarrow & -1120x \color{red}{+105} \color{blue}{-105} \color{blue}{+80x} & = & \color{red}{-80x} +12 \color{blue}{+80x} \color{blue}{-105} \\\Leftrightarrow & -1120x+80x& = & 12-105 \\\Leftrightarrow & \color{red}{-1040} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-1040} & & \\\Leftrightarrow & x = \frac{93}{1040} & & \\ & V = \left\{ \frac{93}{1040} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{4})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{9}{4}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{63}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-63} & = & \color{red}{-140x} +24 \\\Leftrightarrow & 168x \color{red}{-63} \color{blue}{+63} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{+63} \\\Leftrightarrow & 168x+140x& = & 24+63 \\\Leftrightarrow & \color{red}{308} x& = & 87 \\\Leftrightarrow & x = \frac{87}{308} & & \\ & V = \left\{ \frac{87}{308} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-12} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -40x \color{red}{-12} \color{blue}{+12} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+12} \\\Leftrightarrow & -40x+45x& = & 6+12 \\\Leftrightarrow & \color{red}{5} x& = & 18 \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -4x+\frac{5}{4} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-56} & = & \color{red}{-48x} +15 \\\Leftrightarrow & -420x \color{red}{-56} \color{blue}{+56} \color{blue}{+48x} & = & \color{red}{-48x} +15 \color{blue}{+48x} \color{blue}{+56} \\\Leftrightarrow & -420x+48x& = & 15+56 \\\Leftrightarrow & \color{red}{-372} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-372} & & \\\Leftrightarrow & x = \frac{-71}{372} & & \\ & V = \left\{ \frac{-71}{372} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{3})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{10}{3}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{12}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 12x \color{red}{-10} & = & \color{red}{-15x} +2 \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+15x} & = & \color{red}{-15x} +2 \color{blue}{+15x} \color{blue}{+10} \\\Leftrightarrow & 12x+15x& = & 2+10 \\\Leftrightarrow & \color{red}{27} x& = & 12 \\\Leftrightarrow & x = \frac{12}{27} & & \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-20} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 56x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & 56x+21x& = & 3+20 \\\Leftrightarrow & \color{red}{77} x& = & 23 \\\Leftrightarrow & x = \frac{23}{77} & & \\ & V = \left\{ \frac{23}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{5})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{14}{5}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{70}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 70x \color{red}{-14} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 70x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & 70x+15x& = & 8+14 \\\Leftrightarrow & \color{red}{85} x& = & 22 \\\Leftrightarrow & x = \frac{22}{85} & & \\ & V = \left\{ \frac{22}{85} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{20}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-792}{ \color{blue}{66} }x+ \frac{120}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -792x \color{red}{+120} & = & \color{red}{330x} +55 \\\Leftrightarrow & -792x \color{red}{+120} \color{blue}{-120} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{-120} \\\Leftrightarrow & -792x-330x& = & 55-120 \\\Leftrightarrow & \color{red}{-1122} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-1122} & & \\\Leftrightarrow & x = \frac{65}{1122} & & \\ & V = \left\{ \frac{65}{1122} \right\} & \\\end{align}\)