Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-6}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-5x } & = & 2 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-4}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-7x } & = & -2 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+1}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+13x } & = & -5 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+9}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-13x } & = & -1 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-1}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-7x } & = & 15 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+8}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-4x } & = & -4 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-2}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-3x } & = & -7 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)