Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+12}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-9x } & = & -15 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+5}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+13x } & = & -15 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+11}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+2x } & = & -6 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+8}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+2x } & = & -14 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-15}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+10x } & = & 15 \color{red}{ -10x }\color{blue}{+15+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &21x & = &30\\\Leftrightarrow & \color{red}{21}x & = &30\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{30}{21} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-6}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+11x } & = & -15 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+1}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-6x } & = & -6 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+15}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-7x } & = & -4 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &-2x & = &-19\\\Leftrightarrow & \color{red}{-2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+12}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x } & = & 11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-26\\\Leftrightarrow & \color{red}{-16}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-26}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)