Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-10}& = & -14 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10-12x } & = & -14 \color{red}{ +12x }\color{blue}{+10-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-2}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-9x } & = & -2 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-8}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-5x } & = & -5 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-11}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+15x } & = & 4 \color{red}{ -15x }\color{blue}{+11+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-1}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-7x } & = & -9 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-20x & = &-8\\\Leftrightarrow & \color{red}{-20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+5}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+5x } & = & -13 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &16x & = &-18\\\Leftrightarrow & \color{red}{16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+1}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-13x } & = & -4 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+3}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+2x } & = & 14 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)