Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+3}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-9x } & = & -7 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-10\\\Leftrightarrow & \color{red}{-4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-11}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-7x } & = & 9 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-10}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-4x } & = & 11 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+4}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4-2x } & = & -8 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-8}& = & -3 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+6x } & = & -3 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-13}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & 3 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-4}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-10x } & = & 15 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-23x & = &19\\\Leftrightarrow & \color{red}{-23}x & = &19\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{19}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)