Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{24}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+72} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{+72} \color{blue}{-72} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-72} \\\Leftrightarrow & -180x-75x& = & 10-72 \\\Leftrightarrow & \color{red}{-255} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-255} & & \\\Leftrightarrow & x = \frac{62}{255} & & \\ & V = \left\{ \frac{62}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+70} & = & \color{red}{135x} +6 \\\Leftrightarrow & -525x \color{red}{+70} \color{blue}{-70} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{-70} \\\Leftrightarrow & -525x-135x& = & 6-70 \\\Leftrightarrow & \color{red}{-660} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-660} & & \\\Leftrightarrow & x = \frac{16}{165} & & \\ & V = \left\{ \frac{16}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{288}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 288x \color{red}{-16} & = & \color{red}{90x} +81 \\\Leftrightarrow & 288x \color{red}{-16} \color{blue}{+16} \color{blue}{-90x} & = & \color{red}{90x} +81 \color{blue}{-90x} \color{blue}{+16} \\\Leftrightarrow & 288x-90x& = & 81+16 \\\Leftrightarrow & \color{red}{198} x& = & 97 \\\Leftrightarrow & x = \frac{97}{198} & & \\ & V = \left\{ \frac{97}{198} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+10} & = & \color{red}{49x} +8 \\\Leftrightarrow & 70x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & 70x-49x& = & 8-10 \\\Leftrightarrow & \color{red}{21} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+48} & = & \color{red}{297x} +55 \\\Leftrightarrow & 264x \color{red}{+48} \color{blue}{-48} \color{blue}{-297x} & = & \color{red}{297x} +55 \color{blue}{-297x} \color{blue}{-48} \\\Leftrightarrow & 264x-297x& = & 55-48 \\\Leftrightarrow & \color{red}{-33} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-33} & & \\\Leftrightarrow & x = \frac{-7}{33} & & \\ & V = \left\{ \frac{-7}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{10})& = & 2x+\frac{9}{11} \\\Leftrightarrow & 15x-\frac{9}{10}& = & 2x+\frac{9}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1650}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{220}{ \color{blue}{110} }x+ \frac{90}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1650x \color{red}{-99} & = & \color{red}{220x} +90 \\\Leftrightarrow & 1650x \color{red}{-99} \color{blue}{+99} \color{blue}{-220x} & = & \color{red}{220x} +90 \color{blue}{-220x} \color{blue}{+99} \\\Leftrightarrow & 1650x-220x& = & 90+99 \\\Leftrightarrow & \color{red}{1430} x& = & 189 \\\Leftrightarrow & x = \frac{189}{1430} & & \\ & V = \left\{ \frac{189}{1430} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{12}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+36} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 495x \color{red}{+36} \color{blue}{-36} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-36} \\\Leftrightarrow & 495x+231x& = & 44-36 \\\Leftrightarrow & \color{red}{726} x& = & 8 \\\Leftrightarrow & x = \frac{8}{726} & & \\\Leftrightarrow & x = \frac{4}{363} & & \\ & V = \left\{ \frac{4}{363} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -8x+\frac{5}{4} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -8x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{-96x} +15 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{+96x} & = & \color{red}{-96x} +15 \color{blue}{+96x} \color{blue}{-80} \\\Leftrightarrow & 300x+96x& = & 15-80 \\\Leftrightarrow & \color{red}{396} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{396} & & \\ & V = \left\{ \frac{-65}{396} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{-255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-255} & & \\\Leftrightarrow & x = \frac{-86}{255} & & \\ & V = \left\{ \frac{-86}{255} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x- \frac{16}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{-16} & = & \color{red}{140x} +45 \\\Leftrightarrow & 160x \color{red}{-16} \color{blue}{+16} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{+16} \\\Leftrightarrow & 160x-140x& = & 45+16 \\\Leftrightarrow & \color{red}{20} x& = & 61 \\\Leftrightarrow & x = \frac{61}{20} & & \\ & V = \left\{ \frac{61}{20} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+100} & = & \color{red}{245x} +63 \\\Leftrightarrow & 420x \color{red}{+100} \color{blue}{-100} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-100} \\\Leftrightarrow & 420x-245x& = & 63-100 \\\Leftrightarrow & \color{red}{175} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{175} & & \\ & V = \left\{ \frac{-37}{175} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{11})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 704x \color{red}{+64} & = & \color{red}{-792x} +55 \\\Leftrightarrow & 704x \color{red}{+64} \color{blue}{-64} \color{blue}{+792x} & = & \color{red}{-792x} +55 \color{blue}{+792x} \color{blue}{-64} \\\Leftrightarrow & 704x+792x& = & 55-64 \\\Leftrightarrow & \color{red}{1496} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{1496} & & \\ & V = \left\{ \frac{-9}{1496} \right\} & \\\end{align}\)