Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(3x-13=13+4x\)
2. \(14x+2=-15+x\)
3. \(-6x+3=4+x\)
4. \(-x-12=-10+0x\)
5. \(3x-7=-1-8x\)
6. \(13x-2=-1+3x\)
7. \(15x+15=6-14x\)
8. \(-2x+14=-15+x\)
9. \(11x-6=-11-10x\)
10. \(-7x+11=-11+4x\)
11. \(13x-7=12-6x\)
12. \(-4x+9=-10+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-13}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-4x } & = & 13 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-x & = &26\\\Leftrightarrow & \color{red}{-}x & = &26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{26}{-1} \\\Leftrightarrow & \color{green}{ x = -26 } & & \\ & V = \left\{ -26 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-12}& = & -10 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+0x } & = & -10 \color{red}{ +0x }\color{blue}{+12+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-7}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+8x } & = & -1 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-2}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2-3x } & = & -1 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+15}& = & 6 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+14x } & = & 6 \color{red}{ -14x }\color{blue}{-15+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &29x & = &-9\\\Leftrightarrow & \color{red}{29}x & = &-9\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-9}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{29} } & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-29\\\Leftrightarrow & \color{red}{-3}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-29}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{29}{3} } & & \\ & V = \left\{ \frac{29}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-6}& = & -11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+10x } & = & -11 \color{red}{ -10x }\color{blue}{+6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &21x & = &-5\\\Leftrightarrow & \color{red}{21}x & = &-5\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-5}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{21} } & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+11}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-4x } & = & -11 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-22\\\Leftrightarrow & \color{red}{-11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-22}{-11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-7}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x } & = & 12 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)