Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+5}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-13x } & = & -12 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-18x & = &-17\\\Leftrightarrow & \color{red}{-18}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-17}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{17}{18} } & & \\ & V = \left\{ \frac{17}{18} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+10}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10+3x } & = & 11 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+8x } & = & -4 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-11}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-14x } & = & -12 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+3}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-7x } & = & -1 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+9}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-4x } & = & -5 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-19x & = &-14\\\Leftrightarrow & \color{red}{-19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+5}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-5x } & = & 8 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+14}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+7x } & = & -3 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &12x & = &-8\\\Leftrightarrow & \color{red}{12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)