Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{3})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -16x-\frac{8}{3}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-56} & = & \color{red}{147x} +6 \\\Leftrightarrow & -336x \color{red}{-56} \color{blue}{+56} \color{blue}{-147x} & = & \color{red}{147x} +6 \color{blue}{-147x} \color{blue}{+56} \\\Leftrightarrow & -336x-147x& = & 6+56 \\\Leftrightarrow & \color{red}{-483} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-483} & & \\\Leftrightarrow & x = \frac{-62}{483} & & \\ & V = \left\{ \frac{-62}{483} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{6}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+54} & = & \color{red}{495x} +110 \\\Leftrightarrow & -1188x \color{red}{+54} \color{blue}{-54} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{-54} \\\Leftrightarrow & -1188x-495x& = & 110-54 \\\Leftrightarrow & \color{red}{-1683} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-1683} & & \\\Leftrightarrow & x = \frac{-56}{1683} & & \\ & V = \left\{ \frac{-56}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{-40} & = & \color{red}{42x} +15 \\\Leftrightarrow & -96x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +15 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & -96x-42x& = & 15+40 \\\Leftrightarrow & \color{red}{-138} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-138} & & \\\Leftrightarrow & x = \frac{-55}{138} & & \\ & V = \left\{ \frac{-55}{138} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{704}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 704x \color{red}{+80} & = & \color{red}{616x} +99 \\\Leftrightarrow & 704x \color{red}{+80} \color{blue}{-80} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{-80} \\\Leftrightarrow & 704x-616x& = & 99-80 \\\Leftrightarrow & \color{red}{88} x& = & 19 \\\Leftrightarrow & x = \frac{19}{88} & & \\ & V = \left\{ \frac{19}{88} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{15}{8}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{392x} +80 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{-392x} & = & \color{red}{392x} +80 \color{blue}{-392x} \color{blue}{+105} \\\Leftrightarrow & -336x-392x& = & 80+105 \\\Leftrightarrow & \color{red}{-728} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-728} & & \\\Leftrightarrow & x = \frac{-185}{728} & & \\ & V = \left\{ \frac{-185}{728} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{16x} +12 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{-16x} & = & \color{red}{16x} +12 \color{blue}{-16x} \color{blue}{+15} \\\Leftrightarrow & 120x-16x& = & 12+15 \\\Leftrightarrow & \color{red}{104} x& = & 27 \\\Leftrightarrow & x = \frac{27}{104} & & \\ & V = \left\{ \frac{27}{104} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-16} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & -84x+35x& = & 2+16 \\\Leftrightarrow & \color{red}{-49} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-49} & & \\\Leftrightarrow & x = \frac{-18}{49} & & \\ & V = \left\{ \frac{-18}{49} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & 300x+140x& = & 24+75 \\\Leftrightarrow & \color{red}{440} x& = & 99 \\\Leftrightarrow & x = \frac{99}{440} & & \\\Leftrightarrow & x = \frac{9}{40} & & \\ & V = \left\{ \frac{9}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{6})& = & -6x+\frac{5}{2} \\\Leftrightarrow & 35x-\frac{35}{6}& = & -6x+\frac{5}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-35} & = & \color{red}{-36x} +15 \\\Leftrightarrow & 210x \color{red}{-35} \color{blue}{+35} \color{blue}{+36x} & = & \color{red}{-36x} +15 \color{blue}{+36x} \color{blue}{+35} \\\Leftrightarrow & 210x+36x& = & 15+35 \\\Leftrightarrow & \color{red}{246} x& = & 50 \\\Leftrightarrow & x = \frac{50}{246} & & \\\Leftrightarrow & x = \frac{25}{123} & & \\ & V = \left\{ \frac{25}{123} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+110} & = & \color{red}{539x} +35 \\\Leftrightarrow & 1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & 1540x-539x& = & 35-110 \\\Leftrightarrow & \color{red}{1001} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{1001} & & \\ & V = \left\{ \frac{-75}{1001} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{11})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+30} & = & \color{red}{-264x} +77 \\\Leftrightarrow & -825x \color{red}{+30} \color{blue}{-30} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{-30} \\\Leftrightarrow & -825x+264x& = & 77-30 \\\Leftrightarrow & \color{red}{-561} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-561} & & \\\Leftrightarrow & x = \frac{-47}{561} & & \\ & V = \left\{ \frac{-47}{561} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{18}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+126} & = & \color{red}{175x} +15 \\\Leftrightarrow & 420x \color{red}{+126} \color{blue}{-126} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-126} \\\Leftrightarrow & 420x-175x& = & 15-126 \\\Leftrightarrow & \color{red}{245} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{245} & & \\ & V = \left\{ \frac{-111}{245} \right\} & \\\end{align}\)