Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+10}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-13x } & = & -2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+2}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-7x } & = & -6 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+9}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-5x } & = & -5 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+14}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-13x } & = & 14 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+8}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+5x } & = & -2 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+14}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-4x } & = & -9 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-12}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+6x } & = & -4 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-8}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+9x } & = & -15 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &14x & = &-7\\\Leftrightarrow & \color{red}{14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-7}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+10x } & = & -3 \color{red}{ -10x }\color{blue}{+7+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)