Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(10x+15=-14+x\)
2. \(-14x-11=8+x\)
3. \(8x-9=10-15x\)
4. \(-14x+2=4+x\)
5. \(11x+11=14+12x\)
6. \(-10x-13=-3+7x\)
7. \(x+1=-7-12x\)
8. \(-2x-5=5+x\)
9. \(-9x+11=-12+7x\)
10. \(2x+7=2+5x\)
11. \(3x+9=2+4x\)
12. \(-12x-6=13+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &9x & = &-29\\\Leftrightarrow & \color{red}{9}x & = &-29\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-29}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{9} } & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-9}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+15x } & = & 10 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &23x & = &19\\\Leftrightarrow & \color{red}{23}x & = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+11}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-12x } & = & 14 \color{red}{ +12x }\color{blue}{-11-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-13}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-7x } & = & -3 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+1}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+12x } & = & -7 \color{red}{ -12x }\color{blue}{-1+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+11}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-7x } & = & -12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-23\\\Leftrightarrow & \color{red}{-16}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{23}{16} } & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+7}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-5x } & = & 2 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-4x } & = & 2 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)