Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-8}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-3x } & = & -13 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-4}& = & 8 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+12x } & = & 8 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-5x & = &24\\\Leftrightarrow & \color{red}{-5}x & = &24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-7}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & 1 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+3}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-7x } & = & 9 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+7}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-13x } & = & 12 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+2}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-11x } & = & -3 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-11x } & = & -3 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)