Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-2}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-2x } & = & -5 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-9}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-11x } & = & 11 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+13}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-9x } & = & -13 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-26\\\Leftrightarrow & \color{red}{-17}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-26}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-7}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+9x } & = & -13 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &23x & = &-6\\\Leftrightarrow & \color{red}{23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{23} } & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+12}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-7x } & = & 7 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+1}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-8x } & = & 13 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+1}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-12x } & = & 13 \color{red}{ +12x }\color{blue}{-1-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-15}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+5x } & = & 11 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &8x & = &26\\\Leftrightarrow & \color{red}{8}x & = &26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)