Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-12}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-6x } & = & 6 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-1}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-13x } & = & 14 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &-28x & = &15\\\Leftrightarrow & \color{red}{-28}x & = &15\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{15}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{28} } & & \\ & V = \left\{ \frac{-15}{28} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-14x & = &13\\\Leftrightarrow & \color{red}{-14}x & = &13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-14}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+4x } & = & 12 \color{red}{ -4x }\color{blue}{+14+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &17x & = &26\\\Leftrightarrow & \color{red}{17}x & = &26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+13}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+7x } & = & 6 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &22x & = &-7\\\Leftrightarrow & \color{red}{22}x & = &-7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-5}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-6x } & = & 11 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+5}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-8x } & = & -1 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-6}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-9x } & = & -10 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+9}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-11x } & = & -9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-2}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-12x } & = & 6 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)