Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+11}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & 2 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & -5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-10}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-7x } & = & 14 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-20x & = &24\\\Leftrightarrow & \color{red}{-20}x & = &24\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{24}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+11}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-4x } & = & 3 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-3}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-11x } & = & 13 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+14}& = & -4 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+10x } & = & -4 \color{red}{ -10x }\color{blue}{-14+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &9x & = &-18\\\Leftrightarrow & \color{red}{9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-18}{9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-3}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3-11x } & = & 7 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+2}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-7x } & = & -7 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)