Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{2})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{9}{2}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{99}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-99} & = & \color{red}{110x} +12 \\\Leftrightarrow & -264x \color{red}{-99} \color{blue}{+99} \color{blue}{-110x} & = & \color{red}{110x} +12 \color{blue}{-110x} \color{blue}{+99} \\\Leftrightarrow & -264x-110x& = & 12+99 \\\Leftrightarrow & \color{red}{-374} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-374} & & \\\Leftrightarrow & x = \frac{-111}{374} & & \\ & V = \left\{ \frac{-111}{374} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+40} & = & \color{red}{-75x} +12 \\\Leftrightarrow & 90x \color{red}{+40} \color{blue}{-40} \color{blue}{+75x} & = & \color{red}{-75x} +12 \color{blue}{+75x} \color{blue}{-40} \\\Leftrightarrow & 90x+75x& = & 12-40 \\\Leftrightarrow & \color{red}{165} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{165} & & \\ & V = \left\{ \frac{-28}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 630x-175x& = & 20+84 \\\Leftrightarrow & \color{red}{455} x& = & 104 \\\Leftrightarrow & x = \frac{104}{455} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{8})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{15}{8}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+105} & = & \color{red}{504x} +80 \\\Leftrightarrow & 1120x \color{red}{+105} \color{blue}{-105} \color{blue}{-504x} & = & \color{red}{504x} +80 \color{blue}{-504x} \color{blue}{-105} \\\Leftrightarrow & 1120x-504x& = & 80-105 \\\Leftrightarrow & \color{red}{616} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{616} & & \\ & V = \left\{ \frac{-25}{616} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-30} & = & \color{red}{231x} +44 \\\Leftrightarrow & 264x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & 264x-231x& = & 44+30 \\\Leftrightarrow & \color{red}{33} x& = & 74 \\\Leftrightarrow & x = \frac{74}{33} & & \\ & V = \left\{ \frac{74}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{9})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 15x-\frac{20}{9}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{-40} & = & \color{red}{36x} +15 \\\Leftrightarrow & 270x \color{red}{-40} \color{blue}{+40} \color{blue}{-36x} & = & \color{red}{36x} +15 \color{blue}{-36x} \color{blue}{+40} \\\Leftrightarrow & 270x-36x& = & 15+40 \\\Leftrightarrow & \color{red}{234} x& = & 55 \\\Leftrightarrow & x = \frac{55}{234} & & \\ & V = \left\{ \frac{55}{234} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{9})& = & 3x+\frac{7}{6} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 3x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{-16} & = & \color{red}{54x} +21 \\\Leftrightarrow & 144x \color{red}{-16} \color{blue}{+16} \color{blue}{-54x} & = & \color{red}{54x} +21 \color{blue}{-54x} \color{blue}{+16} \\\Leftrightarrow & 144x-54x& = & 21+16 \\\Leftrightarrow & \color{red}{90} x& = & 37 \\\Leftrightarrow & x = \frac{37}{90} & & \\ & V = \left\{ \frac{37}{90} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+264} & = & \color{red}{275x} +30 \\\Leftrightarrow & 1320x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & 1320x-275x& = & 30-264 \\\Leftrightarrow & \color{red}{1045} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{1045} & & \\ & V = \left\{ \frac{-234}{1045} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+24} & = & \color{red}{60x} +45 \\\Leftrightarrow & 160x \color{red}{+24} \color{blue}{-24} \color{blue}{-60x} & = & \color{red}{60x} +45 \color{blue}{-60x} \color{blue}{-24} \\\Leftrightarrow & 160x-60x& = & 45-24 \\\Leftrightarrow & \color{red}{100} x& = & 21 \\\Leftrightarrow & x = \frac{21}{100} & & \\ & V = \left\{ \frac{21}{100} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+66} & = & \color{red}{-385x} +35 \\\Leftrightarrow & 462x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & 462x+385x& = & 35-66 \\\Leftrightarrow & \color{red}{847} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{847} & & \\ & V = \left\{ \frac{-31}{847} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{189x} +30 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & 168x-189x& = & 30-28 \\\Leftrightarrow & \color{red}{-21} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-21} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{15}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-30} & = & \color{red}{42x} +63 \\\Leftrightarrow & 280x \color{red}{-30} \color{blue}{+30} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{+30} \\\Leftrightarrow & 280x-42x& = & 63+30 \\\Leftrightarrow & \color{red}{238} x& = & 93 \\\Leftrightarrow & x = \frac{93}{238} & & \\ & V = \left\{ \frac{93}{238} \right\} & \\\end{align}\)