Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+54} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -378x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & -378x+441x& = & 28-54 \\\Leftrightarrow & \color{red}{63} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{63} & & \\ & V = \left\{ \frac{-26}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & -924x+385x& = & 44+84 \\\Leftrightarrow & \color{red}{-539} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-539} & & \\\Leftrightarrow & x = \frac{-128}{539} & & \\ & V = \left\{ \frac{-128}{539} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x+\frac{12}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-396}{ \color{blue}{44} }x+ \frac{48}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -396x \color{red}{+48} & = & \color{red}{-220x} +33 \\\Leftrightarrow & -396x \color{red}{+48} \color{blue}{-48} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-48} \\\Leftrightarrow & -396x+220x& = & 33-48 \\\Leftrightarrow & \color{red}{-176} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-176} & & \\\Leftrightarrow & x = \frac{15}{176} & & \\ & V = \left\{ \frac{15}{176} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-98} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -294x \color{red}{-98} \color{blue}{+98} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+98} \\\Leftrightarrow & -294x+63x& = & 30+98 \\\Leftrightarrow & \color{red}{-231} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-231} & & \\\Leftrightarrow & x = \frac{-128}{231} & & \\ & V = \left\{ \frac{-128}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{15}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{+75} & = & \color{red}{200x} +48 \\\Leftrightarrow & -480x \color{red}{+75} \color{blue}{-75} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{-75} \\\Leftrightarrow & -480x-200x& = & 48-75 \\\Leftrightarrow & \color{red}{-680} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-680} & & \\\Leftrightarrow & x = \frac{27}{680} & & \\ & V = \left\{ \frac{27}{680} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 240x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & 240x+100x& = & 45+48 \\\Leftrightarrow & \color{red}{340} x& = & 93 \\\Leftrightarrow & x = \frac{93}{340} & & \\ & V = \left\{ \frac{93}{340} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +5 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +5 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 5-6 \\\Leftrightarrow & \color{red}{-119} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-119} & & \\\Leftrightarrow & x = \frac{1}{119} & & \\ & V = \left\{ \frac{1}{119} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+64} & = & \color{red}{120x} +35 \\\Leftrightarrow & -320x \color{red}{+64} \color{blue}{-64} \color{blue}{-120x} & = & \color{red}{120x} +35 \color{blue}{-120x} \color{blue}{-64} \\\Leftrightarrow & -320x-120x& = & 35-64 \\\Leftrightarrow & \color{red}{-440} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-440} & & \\\Leftrightarrow & x = \frac{29}{440} & & \\ & V = \left\{ \frac{29}{440} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{11})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{20}{11}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{60}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{297x} +22 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{+60} \\\Leftrightarrow & 660x-297x& = & 22+60 \\\Leftrightarrow & \color{red}{363} x& = & 82 \\\Leftrightarrow & x = \frac{82}{363} & & \\ & V = \left\{ \frac{82}{363} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{28}{3}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-56} & = & \color{red}{-24x} +9 \\\Leftrightarrow & -168x \color{red}{-56} \color{blue}{+56} \color{blue}{+24x} & = & \color{red}{-24x} +9 \color{blue}{+24x} \color{blue}{+56} \\\Leftrightarrow & -168x+24x& = & 9+56 \\\Leftrightarrow & \color{red}{-144} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-144} & & \\\Leftrightarrow & x = \frac{-65}{144} & & \\ & V = \left\{ \frac{-65}{144} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 16x+\frac{8}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+88} & = & \color{red}{385x} +56 \\\Leftrightarrow & 1232x \color{red}{+88} \color{blue}{-88} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{-88} \\\Leftrightarrow & 1232x-385x& = & 56-88 \\\Leftrightarrow & \color{red}{847} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{847} & & \\ & V = \left\{ \frac{-32}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{-132} \\\Leftrightarrow & -825x+220x& = & 30-132 \\\Leftrightarrow & \color{red}{-605} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-605} & & \\\Leftrightarrow & x = \frac{102}{605} & & \\ & V = \left\{ \frac{102}{605} \right\} & \\\end{align}\)