Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+4}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-13x } & = & -7 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+2}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-7x } & = & 3 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+12}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+5x } & = & 9 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+11}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+5x } & = & 5 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &16x & = &-6\\\Leftrightarrow & \color{red}{16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-6}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+14}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-13x } & = & 2 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+3}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-11x } & = & -3 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-18x & = &-6\\\Leftrightarrow & \color{red}{-18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+10}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-12x } & = & -5 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)