Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{2})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 10x+\frac{25}{2}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+175} & = & \color{red}{42x} +12 \\\Leftrightarrow & 140x \color{red}{+175} \color{blue}{-175} \color{blue}{-42x} & = & \color{red}{42x} +12 \color{blue}{-42x} \color{blue}{-175} \\\Leftrightarrow & 140x-42x& = & 12-175 \\\Leftrightarrow & \color{red}{98} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{98} & & \\ & V = \left\{ \frac{-163}{98} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+70} & = & \color{red}{-539x} +99 \\\Leftrightarrow & -770x \color{red}{+70} \color{blue}{-70} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{-70} \\\Leftrightarrow & -770x+539x& = & 99-70 \\\Leftrightarrow & \color{red}{-231} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-231} & & \\\Leftrightarrow & x = \frac{-29}{231} & & \\ & V = \left\{ \frac{-29}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-264} & = & \color{red}{275x} +15 \\\Leftrightarrow & 660x \color{red}{-264} \color{blue}{+264} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{+264} \\\Leftrightarrow & 660x-275x& = & 15+264 \\\Leftrightarrow & \color{red}{385} x& = & 279 \\\Leftrightarrow & x = \frac{279}{385} & & \\ & V = \left\{ \frac{279}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 4x-\frac{6}{5}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-54} & = & \color{red}{-405x} +20 \\\Leftrightarrow & 180x \color{red}{-54} \color{blue}{+54} \color{blue}{+405x} & = & \color{red}{-405x} +20 \color{blue}{+405x} \color{blue}{+54} \\\Leftrightarrow & 180x+405x& = & 20+54 \\\Leftrightarrow & \color{red}{585} x& = & 74 \\\Leftrightarrow & x = \frac{74}{585} & & \\ & V = \left\{ \frac{74}{585} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{-40} & = & \color{red}{-126x} +27 \\\Leftrightarrow & -288x \color{red}{-40} \color{blue}{+40} \color{blue}{+126x} & = & \color{red}{-126x} +27 \color{blue}{+126x} \color{blue}{+40} \\\Leftrightarrow & -288x+126x& = & 27+40 \\\Leftrightarrow & \color{red}{-162} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-162} & & \\\Leftrightarrow & x = \frac{-67}{162} & & \\ & V = \left\{ \frac{-67}{162} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{+15} & = & \color{red}{-40x} +20 \\\Leftrightarrow & 96x \color{red}{+15} \color{blue}{-15} \color{blue}{+40x} & = & \color{red}{-40x} +20 \color{blue}{+40x} \color{blue}{-15} \\\Leftrightarrow & 96x+40x& = & 20-15 \\\Leftrightarrow & \color{red}{136} x& = & 5 \\\Leftrightarrow & x = \frac{5}{136} & & \\ & V = \left\{ \frac{5}{136} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{77x} +4 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-30} \\\Leftrightarrow & -330x-77x& = & 4-30 \\\Leftrightarrow & \color{red}{-407} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-407} & & \\\Leftrightarrow & x = \frac{26}{407} & & \\ & V = \left\{ \frac{26}{407} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 8x+\frac{12}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+84} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 616x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & 616x+539x& = & 66-84 \\\Leftrightarrow & \color{red}{1155} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{1155} & & \\\Leftrightarrow & x = \frac{-6}{385} & & \\ & V = \left\{ \frac{-6}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{1}{2})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{7}{2}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{21}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-21} & = & \color{red}{24x} +8 \\\Leftrightarrow & -168x \color{red}{-21} \color{blue}{+21} \color{blue}{-24x} & = & \color{red}{24x} +8 \color{blue}{-24x} \color{blue}{+21} \\\Leftrightarrow & -168x-24x& = & 8+21 \\\Leftrightarrow & \color{red}{-192} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-192} & & \\\Leftrightarrow & x = \frac{-29}{192} & & \\ & V = \left\{ \frac{-29}{192} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{6}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+18} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 135x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 135x+105x& = & 50-18 \\\Leftrightarrow & \color{red}{240} x& = & 32 \\\Leftrightarrow & x = \frac{32}{240} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{8}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-80} & = & \color{red}{490x} +63 \\\Leftrightarrow & 840x \color{red}{-80} \color{blue}{+80} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+80} \\\Leftrightarrow & 840x-490x& = & 63+80 \\\Leftrightarrow & \color{red}{350} x& = & 143 \\\Leftrightarrow & x = \frac{143}{350} & & \\ & V = \left\{ \frac{143}{350} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & -2x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-56} & = & \color{red}{-24x} +9 \\\Leftrightarrow & 252x \color{red}{-56} \color{blue}{+56} \color{blue}{+24x} & = & \color{red}{-24x} +9 \color{blue}{+24x} \color{blue}{+56} \\\Leftrightarrow & 252x+24x& = & 9+56 \\\Leftrightarrow & \color{red}{276} x& = & 65 \\\Leftrightarrow & x = \frac{65}{276} & & \\ & V = \left\{ \frac{65}{276} \right\} & \\\end{align}\)