Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-13}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-7x } & = & 11 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-20x & = &24\\\Leftrightarrow & \color{red}{-20}x & = &24\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{24}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+5}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-13x } & = & 13 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+11}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-5x } & = & -2 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-9}& = & 7 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+4x } & = & 7 \color{red}{ -4x }\color{blue}{+9+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-12}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-9x } & = & -13 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+10}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-7}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-11x } & = & -1 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)