Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{15}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+75} & = & \color{red}{385x} +66 \\\Leftrightarrow & 1100x \color{red}{+75} \color{blue}{-75} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-75} \\\Leftrightarrow & 1100x-385x& = & 66-75 \\\Leftrightarrow & \color{red}{715} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{715} & & \\ & V = \left\{ \frac{-9}{715} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-66} & = & \color{red}{231x} +28 \\\Leftrightarrow & 770x \color{red}{-66} \color{blue}{+66} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{+66} \\\Leftrightarrow & 770x-231x& = & 28+66 \\\Leftrightarrow & \color{red}{539} x& = & 94 \\\Leftrightarrow & x = \frac{94}{539} & & \\ & V = \left\{ \frac{94}{539} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-120} \\\Leftrightarrow & 1320x+275x& = & 66-120 \\\Leftrightarrow & \color{red}{1595} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{1595} & & \\ & V = \left\{ \frac{-54}{1595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 4-12 \\\Leftrightarrow & \color{red}{55} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{55} & & \\ & V = \left\{ \frac{-8}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & 240x+70x& = & 15+24 \\\Leftrightarrow & \color{red}{310} x& = & 39 \\\Leftrightarrow & x = \frac{39}{310} & & \\ & V = \left\{ \frac{39}{310} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{21}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+63} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -462x \color{red}{+63} \color{blue}{-63} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{-63} \\\Leftrightarrow & -462x+165x& = & 110-63 \\\Leftrightarrow & \color{red}{-297} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-297} & & \\\Leftrightarrow & x = \frac{-47}{297} & & \\ & V = \left\{ \frac{-47}{297} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -54x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -54x+63x& = & 6-8 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & 4x+\frac{9}{11} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 4x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-132} & = & \color{red}{220x} +45 \\\Leftrightarrow & -825x \color{red}{-132} \color{blue}{+132} \color{blue}{-220x} & = & \color{red}{220x} +45 \color{blue}{-220x} \color{blue}{+132} \\\Leftrightarrow & -825x-220x& = & 45+132 \\\Leftrightarrow & \color{red}{-1045} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-1045} & & \\\Leftrightarrow & x = \frac{-177}{1045} & & \\ & V = \left\{ \frac{-177}{1045} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{-84x} +32 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +32 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & 180x+84x& = & 32+45 \\\Leftrightarrow & \color{red}{264} x& = & 77 \\\Leftrightarrow & x = \frac{77}{264} & & \\\Leftrightarrow & x = \frac{7}{24} & & \\ & V = \left\{ \frac{7}{24} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{2})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -15x-\frac{9}{2}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-63} & = & \color{red}{-56x} +16 \\\Leftrightarrow & -210x \color{red}{-63} \color{blue}{+63} \color{blue}{+56x} & = & \color{red}{-56x} +16 \color{blue}{+56x} \color{blue}{+63} \\\Leftrightarrow & -210x+56x& = & 16+63 \\\Leftrightarrow & \color{red}{-154} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-154} & & \\\Leftrightarrow & x = \frac{-79}{154} & & \\ & V = \left\{ \frac{-79}{154} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{3})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{42x} +21 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & -120x-42x& = & 21+40 \\\Leftrightarrow & \color{red}{-162} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-162} & & \\\Leftrightarrow & x = \frac{-61}{162} & & \\ & V = \left\{ \frac{-61}{162} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-126} & = & \color{red}{245x} +40 \\\Leftrightarrow & 630x \color{red}{-126} \color{blue}{+126} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+126} \\\Leftrightarrow & 630x-245x& = & 40+126 \\\Leftrightarrow & \color{red}{385} x& = & 166 \\\Leftrightarrow & x = \frac{166}{385} & & \\ & V = \left\{ \frac{166}{385} \right\} & \\\end{align}\)