Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+15}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+3x } & = & 9 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &10x & = &-6\\\Leftrightarrow & \color{red}{10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+9}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-11x } & = & 7 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-15}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+13x } & = & 9 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &24x & = &24\\\Leftrightarrow & \color{red}{24}x & = &24\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{24}{24} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-8}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+2x } & = & 12 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-11}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-13x } & = & -6 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-13}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-13x } & = & 2 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+10}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-11x } & = & -8 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-6}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+13x } & = & 12 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &12x & = &18\\\Leftrightarrow & \color{red}{12}x & = &18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-5x } & = & 15 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-17x & = &18\\\Leftrightarrow & \color{red}{-17}x & = &18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+10}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-13x } & = & 11 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)