Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-4}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-13x } & = & 1 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-13}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & -7 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-20x & = &6\\\Leftrightarrow & \color{red}{-20}x & = &6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+5}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-3x } & = & -1 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+2}& = & 5 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+0x } & = & 5 \color{red}{ +0x }\color{blue}{-2+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-1}& = & 4 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-2x } & = & 4 \color{red}{ +2x }\color{blue}{+1-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-7}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-4x } & = & 5 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-9}& = & 9 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+14x } & = & 9 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &29x & = &18\\\Leftrightarrow & \color{red}{29}x & = &18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{18}{29} } & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)