Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-12x+5=11+x\)
2. \(x+13=-10+0x\)
3. \(-4x+1=-2+x\)
4. \(12x-1=-3+x\)
5. \(-15x-11=-14+x\)
6. \(9x+3=-1-4x\)
7. \(10x-7=-3-9x\)
8. \(-15x-4=8+x\)
9. \(x-14=-11-14x\)
10. \(12x+9=-7-11x\)
11. \(-13x+11=13+x\)
12. \(4x-5=-14+7x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & 11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+13}& = & -10 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13+0x } & = & -10 \color{red}{ +0x }\color{blue}{-13+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+3}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+4x } & = & -1 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-7}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+9x } & = & -3 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &19x & = &4\\\Leftrightarrow & \color{red}{19}x & = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-14}& = & -11 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14+14x } & = & -11 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+9}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & -7 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &23x & = &-16\\\Leftrightarrow & \color{red}{23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{23} } & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-5}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-7x } & = & -14 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)