Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-4}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-6x } & = & 8 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+8}& = & -9 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+15x } & = & -9 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &23x & = &-17\\\Leftrightarrow & \color{red}{23}x & = &-17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{23} } & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+10}& = & 9 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+6x } & = & 9 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-x } & = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-10}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-3x } & = & -7 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-2}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-4x } & = & -2 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)