Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-9}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-4x } & = & -10 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-1}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+11x } & = & 3 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &25x & = &4\\\Leftrightarrow & \color{red}{25}x & = &4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-9}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-8x } & = & 9 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-21x & = &18\\\Leftrightarrow & \color{red}{-21}x & = &18\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{18}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+2}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-9x } & = & 5 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+4}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-5x } & = & -2 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-x } & = & -6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-5}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-5x } & = & -2 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+13}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-11x } & = & -5 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-18x & = &-18\\\Leftrightarrow & \color{red}{-18}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-18}{-18} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+14}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-7x } & = & -4 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-15\\\Leftrightarrow & \color{red}{-7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+10}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-9x } & = & -13 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)