Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-2}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+3x } & = & -2 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-13x } & = & 13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-12}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-5x } & = & 3 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-17x & = &15\\\Leftrightarrow & \color{red}{-17}x & = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+15}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-3x } & = & 14 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+15}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15+4x } & = & -1 \color{red}{ -4x }\color{blue}{-15+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & 7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)