Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-8}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-5x } & = & -6 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+1}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x } & = & -1 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-9x } & = & -7 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+2}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+15x } & = & -1 \color{red}{ -15x }\color{blue}{-2+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+2}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-11x } & = & 10 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-21x & = &8\\\Leftrightarrow & \color{red}{-21}x & = &8\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{8}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-3}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-5x } & = & -15 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-5}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-10x } & = & -8 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+14}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-8x } & = & -1 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+7}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+14x } & = & -3 \color{red}{ -14x }\color{blue}{-7+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)