Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-8}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & -4 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-1}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-11x } & = & 8 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+14}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-8x } & = & 14 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-x } & = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &12x & = &3\\\Leftrightarrow & \color{red}{12}x & = &3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+11}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-9x } & = & 7 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-14}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+8x } & = & 13 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &11x & = &27\\\Leftrightarrow & \color{red}{11}x & = &27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-9}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-14x } & = & 7 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-27x & = &16\\\Leftrightarrow & \color{red}{-27}x & = &16\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{16}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{27} } & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)