Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-154} & = & \color{red}{165x} +24 \\\Leftrightarrow & 924x \color{red}{-154} \color{blue}{+154} \color{blue}{-165x} & = & \color{red}{165x} +24 \color{blue}{-165x} \color{blue}{+154} \\\Leftrightarrow & 924x-165x& = & 24+154 \\\Leftrightarrow & \color{red}{759} x& = & 178 \\\Leftrightarrow & x = \frac{178}{759} & & \\ & V = \left\{ \frac{178}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{189x} +6 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -168x-189x& = & 6-56 \\\Leftrightarrow & \color{red}{-357} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-357} & & \\\Leftrightarrow & x = \frac{50}{357} & & \\ & V = \left\{ \frac{50}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 4x+\frac{7}{8} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{72}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-72} & = & \color{red}{160x} +35 \\\Leftrightarrow & -600x \color{red}{-72} \color{blue}{+72} \color{blue}{-160x} & = & \color{red}{160x} +35 \color{blue}{-160x} \color{blue}{+72} \\\Leftrightarrow & -600x-160x& = & 35+72 \\\Leftrightarrow & \color{red}{-760} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-760} & & \\\Leftrightarrow & x = \frac{-107}{760} & & \\ & V = \left\{ \frac{-107}{760} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+16} & = & \color{red}{42x} +7 \\\Leftrightarrow & -96x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +7 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & -96x-42x& = & 7-16 \\\Leftrightarrow & \color{red}{-138} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-138} & & \\\Leftrightarrow & x = \frac{3}{46} & & \\ & V = \left\{ \frac{3}{46} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{+80} & = & \color{red}{-450x} +81 \\\Leftrightarrow & 540x \color{red}{+80} \color{blue}{-80} \color{blue}{+450x} & = & \color{red}{-450x} +81 \color{blue}{+450x} \color{blue}{-80} \\\Leftrightarrow & 540x+450x& = & 81-80 \\\Leftrightarrow & \color{red}{990} x& = & 1 \\\Leftrightarrow & x = \frac{1}{990} & & \\ & V = \left\{ \frac{1}{990} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -252x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -252x+105x& = & 14-18 \\\Leftrightarrow & \color{red}{-147} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-147} & & \\\Leftrightarrow & x = \frac{4}{147} & & \\ & V = \left\{ \frac{4}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-80} & = & \color{red}{392x} +49 \\\Leftrightarrow & 1120x \color{red}{-80} \color{blue}{+80} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{+80} \\\Leftrightarrow & 1120x-392x& = & 49+80 \\\Leftrightarrow & \color{red}{728} x& = & 129 \\\Leftrightarrow & x = \frac{129}{728} & & \\ & V = \left\{ \frac{129}{728} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+56} & = & \color{red}{-315x} +27 \\\Leftrightarrow & 378x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +27 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & 378x+315x& = & 27-56 \\\Leftrightarrow & \color{red}{693} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{693} & & \\ & V = \left\{ \frac{-29}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{30}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2640}{ \color{blue}{88} }x- \frac{240}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2640x \color{red}{-240} & = & \color{red}{616x} +77 \\\Leftrightarrow & 2640x \color{red}{-240} \color{blue}{+240} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+240} \\\Leftrightarrow & 2640x-616x& = & 77+240 \\\Leftrightarrow & \color{red}{2024} x& = & 317 \\\Leftrightarrow & x = \frac{317}{2024} & & \\ & V = \left\{ \frac{317}{2024} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -6x+\frac{10}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+20} & = & \color{red}{-154x} +77 \\\Leftrightarrow & -132x \color{red}{+20} \color{blue}{-20} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{-20} \\\Leftrightarrow & -132x+154x& = & 77-20 \\\Leftrightarrow & \color{red}{22} x& = & 57 \\\Leftrightarrow & x = \frac{57}{22} & & \\ & V = \left\{ \frac{57}{22} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 10x+\frac{15}{4}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{36}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{+15} & = & \color{red}{36x} +10 \\\Leftrightarrow & 40x \color{red}{+15} \color{blue}{-15} \color{blue}{-36x} & = & \color{red}{36x} +10 \color{blue}{-36x} \color{blue}{-15} \\\Leftrightarrow & 40x-36x& = & 10-15 \\\Leftrightarrow & \color{red}{4} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{4} & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{16}{3}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-48} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 108x \color{red}{-48} \color{blue}{+48} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{+48} \\\Leftrightarrow & 108x+45x& = & 10+48 \\\Leftrightarrow & \color{red}{153} x& = & 58 \\\Leftrightarrow & x = \frac{58}{153} & & \\ & V = \left\{ \frac{58}{153} \right\} & \\\end{align}\)