Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -35x+\frac{21}{10}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-3150}{ \color{blue}{90} }x+ \frac{189}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -3150x \color{red}{+189} & = & \color{red}{810x} +100 \\\Leftrightarrow & -3150x \color{red}{+189} \color{blue}{-189} \color{blue}{-810x} & = & \color{red}{810x} +100 \color{blue}{-810x} \color{blue}{-189} \\\Leftrightarrow & -3150x-810x& = & 100-189 \\\Leftrightarrow & \color{red}{-3960} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-3960} & & \\\Leftrightarrow & x = \frac{89}{3960} & & \\ & V = \left\{ \frac{89}{3960} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 9x-\frac{15}{11}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{198}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 198x \color{red}{-30} & = & \color{red}{44x} +77 \\\Leftrightarrow & 198x \color{red}{-30} \color{blue}{+30} \color{blue}{-44x} & = & \color{red}{44x} +77 \color{blue}{-44x} \color{blue}{+30} \\\Leftrightarrow & 198x-44x& = & 77+30 \\\Leftrightarrow & \color{red}{154} x& = & 107 \\\Leftrightarrow & x = \frac{107}{154} & & \\ & V = \left\{ \frac{107}{154} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{12}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{-12} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 66x \color{red}{-12} \color{blue}{+12} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{+12} \\\Leftrightarrow & 66x+55x& = & 5+12 \\\Leftrightarrow & \color{red}{121} x& = & 17 \\\Leftrightarrow & x = \frac{17}{121} & & \\ & V = \left\{ \frac{17}{121} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{720}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 720x \color{red}{-72} & = & \color{red}{-150x} +35 \\\Leftrightarrow & 720x \color{red}{-72} \color{blue}{+72} \color{blue}{+150x} & = & \color{red}{-150x} +35 \color{blue}{+150x} \color{blue}{+72} \\\Leftrightarrow & 720x+150x& = & 35+72 \\\Leftrightarrow & \color{red}{870} x& = & 107 \\\Leftrightarrow & x = \frac{107}{870} & & \\ & V = \left\{ \frac{107}{870} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 6x+\frac{9}{7} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 6x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-126}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{42}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -126x \color{red}{-30} & = & \color{red}{42x} +9 \\\Leftrightarrow & -126x \color{red}{-30} \color{blue}{+30} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{+30} \\\Leftrightarrow & -126x-42x& = & 9+30 \\\Leftrightarrow & \color{red}{-168} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-168} & & \\\Leftrightarrow & x = \frac{-13}{56} & & \\ & V = \left\{ \frac{-13}{56} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{11})& = & -4x+\frac{3}{11} \\\Leftrightarrow & 15x+\frac{12}{11}& = & -4x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+12} & = & \color{red}{-44x} +3 \\\Leftrightarrow & 165x \color{red}{+12} \color{blue}{-12} \color{blue}{+44x} & = & \color{red}{-44x} +3 \color{blue}{+44x} \color{blue}{-12} \\\Leftrightarrow & 165x+44x& = & 3-12 \\\Leftrightarrow & \color{red}{209} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{209} & & \\ & V = \left\{ \frac{-9}{209} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-40} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 270x \color{red}{-40} \color{blue}{+40} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{+40} \\\Leftrightarrow & 270x+225x& = & 54+40 \\\Leftrightarrow & \color{red}{495} x& = & 94 \\\Leftrightarrow & x = \frac{94}{495} & & \\ & V = \left\{ \frac{94}{495} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-50} & = & \color{red}{-385x} +88 \\\Leftrightarrow & -330x \color{red}{-50} \color{blue}{+50} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{+50} \\\Leftrightarrow & -330x+385x& = & 88+50 \\\Leftrightarrow & \color{red}{55} x& = & 138 \\\Leftrightarrow & x = \frac{138}{55} & & \\ & V = \left\{ \frac{138}{55} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+154} & = & \color{red}{-99x} +12 \\\Leftrightarrow & 462x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +12 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & 462x+99x& = & 12-154 \\\Leftrightarrow & \color{red}{561} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{561} & & \\ & V = \left\{ \frac{-142}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{35}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+35} & = & \color{red}{-9x} +10 \\\Leftrightarrow & 84x \color{red}{+35} \color{blue}{-35} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{-35} \\\Leftrightarrow & 84x+9x& = & 10-35 \\\Leftrightarrow & \color{red}{93} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{93} & & \\ & V = \left\{ \frac{-25}{93} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x-\frac{16}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-80} & = & \color{red}{275x} +44 \\\Leftrightarrow & -660x \color{red}{-80} \color{blue}{+80} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{+80} \\\Leftrightarrow & -660x-275x& = & 44+80 \\\Leftrightarrow & \color{red}{-935} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-935} & & \\\Leftrightarrow & x = \frac{-124}{935} & & \\ & V = \left\{ \frac{-124}{935} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{12}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-60} & = & \color{red}{220x} +66 \\\Leftrightarrow & -825x \color{red}{-60} \color{blue}{+60} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{+60} \\\Leftrightarrow & -825x-220x& = & 66+60 \\\Leftrightarrow & \color{red}{-1045} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-1045} & & \\\Leftrightarrow & x = \frac{-126}{1045} & & \\ & V = \left\{ \frac{-126}{1045} \right\} & \\\end{align}\)