Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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