Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-9x } & = & 14 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-14}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-5x } & = & -3 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+5}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-11x } & = & -12 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+13}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-11x } & = & 7 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+14}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+2x } & = & -2 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & -11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-12}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-13x } & = & -2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)