Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+4}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-7x } & = & 8 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-5}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x } & = & -13 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-15}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15+6x } & = & -6 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-2}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x } & = & 15 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-28x & = &17\\\Leftrightarrow & \color{red}{-28}x & = &17\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{17}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{28} } & & \\ & V = \left\{ \frac{-17}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+11}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-9x } & = & -1 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+1}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-4x } & = & -15 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+2}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-8x } & = & -15 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-15}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-4x } & = & 15 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-7x & = &30\\\Leftrightarrow & \color{red}{-7}x & = &30\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{30}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{7} } & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-4}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4+13x } & = & -10 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &21x & = &-6\\\Leftrightarrow & \color{red}{21}x & = &-6\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-6}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)