Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-11}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+2x } & = & 2 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x } & = & 7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-5}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-11x } & = & -2 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+5}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-12x } & = & 6 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-3}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & 1 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+5}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+13x } & = & -5 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-10}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-7x } & = & 6 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-9}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9+13x } & = & 1 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)