Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-11}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+5x } & = & -15 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+7}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & 3 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+15}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-5x } & = & 13 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+6}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-10x } & = & 15 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-6}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-11x } & = & -12 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-18x & = &-6\\\Leftrightarrow & \color{red}{-18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-3}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-14x } & = & -6 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-16x & = &24\\\Leftrightarrow & \color{red}{-16}x & = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-1}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+2x } & = & 2 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-14}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-11x } & = & 4 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+11}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+8x } & = & 6 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)