Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-x } & = & -8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+3}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-11x } & = & -5 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-11}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x } & = & -13 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-14}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-13x } & = & 15 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-x & = &29\\\Leftrightarrow & \color{red}{-}x & = &29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{29}{-1} \\\Leftrightarrow & \color{green}{ x = -29 } & & \\ & V = \left\{ -29 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+15}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+5x } & = & -5 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-7}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+9x } & = & -4 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &23x & = &3\\\Leftrightarrow & \color{red}{23}x & = &3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+6}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+14x } & = & -2 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &29x & = &-8\\\Leftrightarrow & \color{red}{29}x & = &-8\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-8}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{29} } & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-8}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+10x } & = & 13 \color{red}{ -10x }\color{blue}{+8+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &21x & = &21\\\Leftrightarrow & \color{red}{21}x & = &21\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{21}{21} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)