Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-5}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-9x } & = & -2 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+6}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+13x } & = & -13 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &22x & = &-19\\\Leftrightarrow & \color{red}{22}x & = &-19\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-19}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{22} } & & \\ & V = \left\{ \frac{-19}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+11x } & = & 2 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-11}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-13x } & = & 12 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 1 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-9x & = &24\\\Leftrightarrow & \color{red}{-9}x & = &24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-26\\\Leftrightarrow & \color{red}{-8}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+8}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-10x } & = & 5 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-6}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-9x } & = & -4 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-22x & = &2\\\Leftrightarrow & \color{red}{-22}x & = &2\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{2}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)