Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-5x+6=13+x\)
2. \(-10x-9=11+7x\)
3. \(2x-11=-2+x\)
4. \(-2x+8=-2+x\)
5. \(10x+8=-13+x\)
6. \(8x+13=11+x\)
7. \(x-12=-7-7x\)
8. \(-7x+10=9+x\)
9. \(6x+13=-3-11x\)
10. \(-8x+4=-7+x\)
11. \(-3x-5=14+4x\)
12. \(7x+1=-5+10x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-9}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-7x } & = & 11 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & -13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+7x } & = & -7 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+13}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+11x } & = & -3 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-5}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-4x } & = & 14 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+1}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-10x } & = & -5 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)