Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-9}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+13x } & = & -8 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+15}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+9x } & = & 12 \color{red}{ -9x }\color{blue}{-15+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &14x & = &-3\\\Leftrightarrow & \color{red}{14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-1}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+2x } & = & 15 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+9}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-13x } & = & -6 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &2x & = &-15\\\Leftrightarrow & \color{red}{2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-15}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-5x } & = & 5 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-7x & = &20\\\Leftrightarrow & \color{red}{-7}x & = &20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-3}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+11x } & = & -9 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &26x & = &-6\\\Leftrightarrow & \color{red}{26}x & = &-6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+2}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-10x } & = & -3 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+1}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-4x } & = & 11 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+10}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-14x } & = & -10 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-23x & = &-20\\\Leftrightarrow & \color{red}{-23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-7x & = &27\\\Leftrightarrow & \color{red}{-7}x & = &27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{7} } & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+9}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+8x } & = & -7 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)