Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-15x-13=-12+13x\)
2. \(3x+14=-8+2x\)
3. \(4x+8=3-3x\)
4. \(-12x-2=-2+x\)
5. \(-4x+12=-4+13x\)
6. \(-2x-11=-11+x\)
7. \(x+4=-7+0x\)
8. \(14x+1=13+9x\)
9. \(8x-10=-14-15x\)
10. \(-11x-9=-11+x\)
11. \(-4x-6=8+9x\)
12. \(-x+1=12+5x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-13}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-13x } & = & -12 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+14}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-2x } & = & -8 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+8}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+3x } & = & 3 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-13x } & = & -4 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-16\\\Leftrightarrow & \color{red}{-17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+4}& = & -7 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+0x } & = & -7 \color{red}{ +0x }\color{blue}{-4+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+1}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-9x } & = & 13 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-10}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+15x } & = & -14 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-6}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-9x } & = & 8 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+1}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-5x } & = & 12 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)