Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-4}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-8x } & = & -2 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-8}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+5x } & = & -5 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &16x & = &3\\\Leftrightarrow & \color{red}{16}x & = &3\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{3}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+11}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-6x } & = & -15 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-x & = &-26\\\Leftrightarrow & \color{red}{-}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-13}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-11x } & = & -11 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-4}& = & 11 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+8x } & = & 11 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &17x & = &15\\\Leftrightarrow & \color{red}{17}x & = &15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+4}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-5x } & = & -7 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+9}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-8x } & = & 1 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-10}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10+13x } & = & 6 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+2}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-5x } & = & -8 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)