Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+4}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x } & = & -13 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-24\\\Leftrightarrow & \color{red}{-9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+12}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x } & = & -13 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &4x & = &-25\\\Leftrightarrow & \color{red}{4}x & = &-25\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-25}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-4}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-3x } & = & -3 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-13}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+5x } & = & 8 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-2}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+9x } & = & -1 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-15}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-5x } & = & -8 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)