Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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