Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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