Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-12x & = &26\\\Leftrightarrow & \color{red}{-12}x & = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-8}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-11x } & = & -11 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-10}& = & -9 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+10x } & = & -9 \color{red}{ -10x }\color{blue}{+10+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &21x & = &1\\\Leftrightarrow & \color{red}{21}x & = &1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+11}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-7x } & = & 1 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-7x } & = & 11 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)