Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-14x } & = & 14 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-1}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-8x } & = & -5 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-2}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-3x } & = & -14 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & -2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-x } & = & -1 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &12x & = &-13\\\Leftrightarrow & \color{red}{12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+11}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-4x } & = & 14 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-3}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-14x } & = & -5 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-23x & = &-2\\\Leftrightarrow & \color{red}{-23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-5x } & = & -8 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)