Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{6})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{10}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-25} & = & \color{red}{42x} +10 \\\Leftrightarrow & 90x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +10 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & 90x-42x& = & 10+25 \\\Leftrightarrow & \color{red}{48} x& = & 35 \\\Leftrightarrow & x = \frac{35}{48} & & \\ & V = \left\{ \frac{35}{48} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{15}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+45} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 396x \color{red}{+45} \color{blue}{-45} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-45} \\\Leftrightarrow & 396x+165x& = & 88-45 \\\Leftrightarrow & \color{red}{561} x& = & 43 \\\Leftrightarrow & x = \frac{43}{561} & & \\ & V = \left\{ \frac{43}{561} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{9})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -10x-\frac{25}{9}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-175} & = & \color{red}{-441x} +45 \\\Leftrightarrow & -630x \color{red}{-175} \color{blue}{+175} \color{blue}{+441x} & = & \color{red}{-441x} +45 \color{blue}{+441x} \color{blue}{+175} \\\Leftrightarrow & -630x+441x& = & 45+175 \\\Leftrightarrow & \color{red}{-189} x& = & 220 \\\Leftrightarrow & x = \frac{220}{-189} & & \\\Leftrightarrow & x = \frac{-220}{189} & & \\ & V = \left\{ \frac{-220}{189} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{294x} +35 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-180} \\\Leftrightarrow & 1260x-294x& = & 35-180 \\\Leftrightarrow & \color{red}{966} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{966} & & \\ & V = \left\{ \frac{-145}{966} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -240x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & -240x+105x& = & 18+40 \\\Leftrightarrow & \color{red}{-135} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-135} & & \\\Leftrightarrow & x = \frac{-58}{135} & & \\ & V = \left\{ \frac{-58}{135} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+64} & = & \color{red}{-252x} +35 \\\Leftrightarrow & -560x \color{red}{+64} \color{blue}{-64} \color{blue}{+252x} & = & \color{red}{-252x} +35 \color{blue}{+252x} \color{blue}{-64} \\\Leftrightarrow & -560x+252x& = & 35-64 \\\Leftrightarrow & \color{red}{-308} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-308} & & \\\Leftrightarrow & x = \frac{29}{308} & & \\ & V = \left\{ \frac{29}{308} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{16}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+80} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -660x \color{red}{+80} \color{blue}{-80} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-80} \\\Leftrightarrow & -660x+275x& = & 66-80 \\\Leftrightarrow & \color{red}{-385} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-385} & & \\\Leftrightarrow & x = \frac{2}{55} & & \\ & V = \left\{ \frac{2}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 24x-\frac{12}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-84} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 1848x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & 1848x+385x& = & 44+84 \\\Leftrightarrow & \color{red}{2233} x& = & 128 \\\Leftrightarrow & x = \frac{128}{2233} & & \\ & V = \left\{ \frac{128}{2233} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{4})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+15} & = & \color{red}{28x} +18 \\\Leftrightarrow & 60x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +18 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & 60x-28x& = & 18-15 \\\Leftrightarrow & \color{red}{32} x& = & 3 \\\Leftrightarrow & x = \frac{3}{32} & & \\ & V = \left\{ \frac{3}{32} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{11})& = & 3x+\frac{7}{4} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{-40} & = & \color{red}{132x} +77 \\\Leftrightarrow & 880x \color{red}{-40} \color{blue}{+40} \color{blue}{-132x} & = & \color{red}{132x} +77 \color{blue}{-132x} \color{blue}{+40} \\\Leftrightarrow & 880x-132x& = & 77+40 \\\Leftrightarrow & \color{red}{748} x& = & 117 \\\Leftrightarrow & x = \frac{117}{748} & & \\ & V = \left\{ \frac{117}{748} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-98x} +35 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & 420x+98x& = & 35+60 \\\Leftrightarrow & \color{red}{518} x& = & 95 \\\Leftrightarrow & x = \frac{95}{518} & & \\ & V = \left\{ \frac{95}{518} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{8})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-160}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-75} & = & \color{red}{-160x} +72 \\\Leftrightarrow & -600x \color{red}{-75} \color{blue}{+75} \color{blue}{+160x} & = & \color{red}{-160x} +72 \color{blue}{+160x} \color{blue}{+75} \\\Leftrightarrow & -600x+160x& = & 72+75 \\\Leftrightarrow & \color{red}{-440} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-440} & & \\\Leftrightarrow & x = \frac{-147}{440} & & \\ & V = \left\{ \frac{-147}{440} \right\} & \\\end{align}\)