Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-x } & = & -10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &2x & = &-16\\\Leftrightarrow & \color{red}{2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-16}{2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-9x } & = & -2 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-14}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-13x } & = & 3 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+8}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-13x } & = & -2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-28x & = &-10\\\Leftrightarrow & \color{red}{-28}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-10}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+7}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-9x } & = & -11 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-18\\\Leftrightarrow & \color{red}{-17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+12}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-9x } & = & -4 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-16\\\Leftrightarrow & \color{red}{-17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &12x & = &-30\\\Leftrightarrow & \color{red}{12}x & = &-30\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-30}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+2}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+13x } & = & -15 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &22x & = &-17\\\Leftrightarrow & \color{red}{22}x & = &-17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{22} } & & \\ & V = \left\{ \frac{-17}{22} \right\} & \\\end{align}\)