Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-7}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+6x } & = & 3 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-12}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-12x } & = & -7 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-9}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-7x } & = & 8 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-1}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 9 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-25x & = &10\\\Leftrightarrow & \color{red}{-25}x & = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+4}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & 2 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-3}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+11x } & = & 6 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &25x & = &9\\\Leftrightarrow & \color{red}{25}x & = &9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+15}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-9x } & = & 15 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-19\\\Leftrightarrow & \color{red}{-8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+14}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+2x } & = & 14 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)