Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+14}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+8x } & = & 5 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+3}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+12x } & = & -7 \color{red}{ -12x }\color{blue}{-3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &2x & = &15\\\Leftrightarrow & \color{red}{2}x & = &15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-1}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & 13 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+9}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+8x } & = & 7 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-13}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-10x } & = & 1 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-19x & = &14\\\Leftrightarrow & \color{red}{-19}x & = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+14}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-11x } & = & 6 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+7}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+9x } & = & 1 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+5}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & -10 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+1}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-7x } & = & 4 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-2}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-11x } & = & 15 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)