Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+6}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-7x } & = & 7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+8}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & -8 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-7}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-13x } & = & 9 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-11}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-11x } & = & 10 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-4x & = &21\\\Leftrightarrow & \color{red}{-4}x & = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)